Question

if 4x + 3y / 4x - 3y = 7/4 using properties of proportion find value of 2x² - 11y² / 2x² + 11 y² ​

Answer 1

The value of 2x^2- 11y^2/2x^2+ 11y^2 is 3/19

$\frac{4x+3y}{4x-3y} = \frac{7}{4}$

Using componendo and dividendo

$\frac{4x+3y + 4x -3y} {4x + 3y - 4x+3y} = \frac{11}{3}$

$\frac{8x}{6y} = \frac{11}{3}$

$\frac{4x}{3y} = \frac{11}{3}$

$\frac{x}{y} = \frac{11}{4}$

Squaring both sides

$\frac{x^{2} }{y^{2} } = \frac{121}{16}$

Shifting 2 from RHS denom to RHS num and 11 from RHS num to LHS denom

$\frac{2x^{2} }{11y^{2} } = \frac{11}{8}$

Applying componendo and dividendo

$\frac{2x^{2} - 11y^{2}}{2x^{2} + 11y^{2} } = \frac{3}{19}$