#### Question

If (7m +8n)(7p - 8q) = (7m - 8n)(7p + 8q), then prove that m: n = p: q

#### Solution

(7m +8n)(7p - 8q) = (7m - 8n)c

`=> (7"m" +8"n")/(7"m" - 8"n") = (7"p" + 8"q")/(7"p" - 8"q")`

Applying componendo and dividendo,

`(7"m" + 8"n" + 7"m" - 8"n")/(7"m" + 8"m" - 7"m" + 8"n") = (7"p" + 8"q" + 7"m" - 8"q")/(7"m" + 8"q" - 7"m" + 8"q")`

`=> (14 "m")/(16 "n") = (14"p")/(16"q")`

Dividing both sides by `14/16`

`"m"/"n" = "p"/"q"`

Hence. m:n = p : q .

Is there an error in this question or solution?

Solution 1f (7m +Bn)(7p-bq) = (7m-bn)(7p+Bq), Then Prove that M: N = P: Concept: Componendo and Dividendo Properties.