Question

Please help asap I’m not very sure how to do this

Answer 1

${a}^{2} + {b}^{2} = 6ab \\ \\ add \: 2ab \\ \\ {a}^{2} + {b}^{2} + 2ab = 8ab \\ \\ {(a + b)}^{2} = 8ab...... < 1 > \\ \\ subtract \: 2ab \\ \\ {a}^{2} + {b}^{2} - 2ab = 4ab \\ \\ {(b - a)}^{2} = 4ab....... < 2 > \\ since \: \: b - a > 0 \\ \\ \frac{ < 1 > }{ < 2 > } \\ \\ {( \frac{a + b}{b - a}) }^{2} = 2 \\ \\ \frac{a + b}{b - a} = \sqrt{2} \\ \\ \frac{a + b}{a - b} = - \sqrt{2}$

hope it helps

Answer 2

Step-by-step explanation:

Let,

a+b ÷ a-b=x

Squaring both sides

(a+b)^2 ÷ (a-b)^2 = x^2

a^2 + b^2 + 2ab ÷ a^2 + b^2 - 2ab = x^2

Since, a^2 + b^2 = 6ab

6ab +2ab ÷ 6ab -2ab = x^2

8ab/4ab = x^2

x^2 = 2

x = square root of 2