Question

55. If 3x = 4y, the value of (x + y)^2 : (x - y)^2 is:
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Answer 1

`\large\boxed{(x+y)^2:(x-y)^2=49}`

Explanation:

`3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=(y)/(3)\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=(7y)/(3)\qquad(**)\\------------------`

`(x+y)^2:(x-y)^2=((x+y)^2)/((x-y)^2)\qquad\text{use}\ \left((a)/(b)\right)^n=(a^n)/(b^n)\\\\=\left((x+y)/(x-y)\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(((7y)/(3))/((y)/(3))\right)^2=\left((7y)/(3)\cdot(3)/(y)\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49`