Question

If 2x² - 2y² = 125 and x - y =2.5, find the value of x+y

Answer 1

SOLUTION :

2x^2-2y^2=125

2(x+y) (x-y) =125

5(x+y) =125

x+y= 25

Answer 2

AnswEr:-

Your Answer Is 25.

ExplanaTion:-

Given:-

$\tt\longrightarrow2 {x}^{2} - 2 {y}^{2} = 125...(1). \\ \\ \tt \: and \\ \\ \tt\longrightarrow x - y = 2.5...(2).$

To Find:-

• The value of x+y.

IDs Used:-

$\bullet{a}^{2} - {b}^{2} = (a + b)(a - b).$

So Here,

$\tt\mapsto2 {x}^{2} - 2 {y}^{2} = 125. \\ \\ \tt\mapsto2( {x}^{2} - {y}^{2} ) = 125. \\ \\ \tt(taking \: \: 2 \: \: as \: \: common). \\ \\ \tt\mapsto {x}^{2} - {y}^{2} = \frac{125}{2} . \\ \\ \tt\mapsto {x}^{2} - {y}^{2} = 62.5 \\ \\ \tt\mapsto(x + y)(x - y) = 62.5 \\ \\\tt(using \: \: id) \\ \\ \tt\mapsto(x +y)(2.5) = 62.5 \\ \\ \tt(from \: \: (2)). \\ \\ \tt\mapsto x + y = \frac{62\cancel{.} \: 5}{2\cancel{.} \: 5} \\ \\ \tt\mapsto x + y = \cancel\frac{625}{25} . \\ \\ \tt\mapsto x + y = 25.$

$\therefore$ The required value of x+y is 25.