Question

(a+b)^2x^2-8(a^2-b^2)x-20(a-b)^2=0

Answer 1

Answer:

x = (4±6) (a-b) / (a+b)

i.e.

x = -2 (a-b) / (a+b)   OR    x = 10 (a-b) / (a+b)

Hope this helps.

(a+b)²x² - 8(a²-b²)x - 20(a-b)² = 0

=> (a+b)²x² - 8(a-b)(a+b)x = 20(a-b)²

=> ( (a+b)x  - 4(a-b) )² = 20(a-b)² + 4²(a-b)²

=> ( (a+b)x - 4(a-b) )² = 36(a-b)²

=> (a+b)x - 4(a-b) = ±6(a-b)

=> (a+b)x = (4±6)(a-b)

=> x = (4±6)(a-b)/(a+b)