Question

Ax2+by2/ax2-by2=77/13 xy2+ab2/xy2-ab2=17/7 find the value of x2:b2​

Answer 1

x² : b² = 3 : 2

Explanation:

Given,

(ax² + by²)/(ax² - by²) = 77/13

or, (x²/y² + b/a)/(x²/y² - b/a) = 77/13

or, 77 (x²/y² - b/a) = 13 (x²/y² + b/a)

or, (77 - 13) x²/y² = (13 + 77) b/a

or, 64 x²/y² = 90 b/a ..... (1)

(xy² + ab²)/(xy² - ab²) = 17/7

or, 17 (xy² - ab²) = 7 (xy² + ab²)

or, (17 - 7) xy² = (7 + 17) ab²

or, 10xy² = 24ab²

or, y² = 24ab² / 10x ..... (2)

From (1) and (2), we get

64x²/(24ab² / 10x) = 90 b/a

or, 640x³ / 24ab² = 90b / a

or, x³ / b³ = 27 / 8

or, x/b = 3/2

or, x²/b² = 3/2

∴ x² : b² = 3 : 2