VRAE oor vraestel 1: Gemengde getalpatrone

Indien a, b, c 'n rekenkundige ry vorm en x, y,z vorm 'n meetkundige ry, toon aan dat: $x to the power of b minus c end exponent. y to the power of c minus a end exponent. z to the power of a minus b end exponent equals 1$

Re: Gemengde getalpatrone

by Marna Zuhlsdorff - Sunday, 7 June 2020, 4:30 AM

Hi Moné

Yikes, hierdie lyk nogals na 'n rowwe som!
Toe ek myself net eers kalmeer het (",) het ek gelukkig gesien hy is nie só moeilik nie...ek moes net my stappe volg.
Baie dankie vir hierdie som - dis regtig 'n goeie een! Ek het sommer 'n video ook van hom gemaak - click hier.

Hier is my oplossing:
Eers doen ons bietjie voorbereiding...

$table row cell RR colon straight a semicolon straight b semicolon straight c end cell row cell T subscript 2 minus T subscript 1 equals T subscript 3 minus T subscript 2 end cell row cell b minus a equals c minus b end cell row cell negative open parentheses a minus b close parentheses equals negative open parentheses b minus c close parentheses end cell row cell a minus b equals b minus c end cell row cell therefore stel space b minus c equals a minus b end cell row cell ook space as end cell row cell a minus b equals b minus c end cell row cell c equals b plus b minus a end cell row cell c equals 2 b minus a end cell end table$

$table row cell MR colon straight x semicolon straight y semicolon straight z end cell row cell T subscript 2 over T subscript 1 equals T subscript 3 over T subscript 2 end cell row cell y over x equals z over y end cell row cell y squared over x equals z end cell end table$

Nou kan ons die som doen

$table row cell L K equals x to the power of b minus c end exponent. y to the power of c minus a end exponent. z to the power of a minus b end exponent end cell blank blank blank row cell equals x to the power of a minus b end exponent. y to the power of open parentheses 2 b minus a close parentheses minus a end exponent. z to the power of a minus b end exponent end cell blank blank cell stel space bold italic b bold minus bold italic c bold equals bold italic a bold minus bold italic b space en space bold italic c bold equals bold 2 bold italic b bold minus bold italic a end cell row cell equals x to the power of a minus b end exponent. y to the power of 2 b minus 2 a end exponent. z to the power of a minus b end exponent end cell blank blank cell v e r e e n v o u d i g end cell row cell equals open parentheses x. z close parentheses to the power of a minus b end exponent y to the power of 2 b minus 2 a end exponent end cell blank blank cell e k s p o n e n t space w e t colon space straight A to the power of x. B to the power of x equals open parentheses AB close parentheses to the power of x end cell row cell equals open parentheses x. y squared over x close parentheses to the power of a minus b end exponent y to the power of 2 b minus 2 a end exponent end cell blank blank cell stel space bold z bold equals bold y to the power of bold 2 over bold x end cell row cell equals open parentheses up diagonal strike x. fraction numerator y squared over denominator up diagonal strike x end fraction close parentheses to the power of a minus b end exponent y to the power of 2 b minus 2 a end exponent end cell blank blank cell k a n s e l l e e r end cell row cell equals open parentheses y squared close parentheses to the power of a minus b end exponent y to the power of 2 b minus 2 a end exponent end cell blank blank cell v e r e e n v o u d i g end cell row cell equals y to the power of 2 a minus 2 b end exponent y to the power of 2 b minus 2 a end exponent end cell blank blank cell e k s p o n e n t space w e t colon space open parentheses straight A to the power of x close parentheses to the power of y equals A to the power of x y end exponent end cell row cell equals y to the power of open parentheses 2 a minus 2 b close parentheses plus open parentheses 2 b minus 2 a close parentheses end exponent end cell blank blank cell e k s p o n e n t space w e t colon space A to the power of x. A to the power of y equals A to the power of x plus y end exponent end cell row cell equals y to the power of 2 a minus 2 b minus 2 b plus 2 a end exponent end cell blank blank blank row cell equals y to the power of 0 end cell blank blank blank row cell equals 1 end cell blank blank blank row cell equals R K end cell blank blank blank end table$

Laat my asb weet as iets onduidelik is.