Question

7a+2b/7a-2b = 5/3 find a:b & a2 + b2 / a2-b2

Answer 1

Answer:

a/b = 8/7

Step-by-step explanation:

21a + 6b = 35a - 10b

16 b = 35-21a

a/b = 8/7

a: b = 8:7

a² + b² = 113

a²- b² = 15

Answer 2

Answer:

$a : b= 8:7$ ,  $\frac{a^{2} +b^{2}}{a^{2} -b^{2}} = 7.53$

Given :

$\frac{7a+2b}{7a-2b} =\frac{5}{3}$   --> (1)

Step by Step Explanation :

First of all, We use cross multiplication for equation (1).

$(7a+2b)(3) = (7a-2b)(5)$

$21a+6b = 35a-10b$

$10b+6b = 35a-21a$

$16b = 14a$

$\frac{16}{14} = \frac{a}{b}$

$\frac{8}{7} = \frac{a}{b}$

Therefore , A value and B value is

$a=8 , b=7$

Then,

$a^{2} +b^{2} = 8^{2}+ 7^{2}$

$8^{2}+ 7^{2} = 64 + 49 = 113$

$a^{2} -b^{2} = 8^{2}- 7^{2}$

$8^{2}- 7^{2}= 64 - 49= 15$

Therefore,

$\frac{a^{2} +b^{2}}{a^{2} -b^{2}} = \frac{113}{15}$

$\frac{113}{15}= 7.53$

So, Answers are..

$\frac{a^{2} +b^{2}}{a^{2} -b^{2}} = 7.53$

$a=8 , b=7$