If 2x2 – 7xy + 3y2 = 0, then the value of x : y is(a) 3 : 2 (b) 2 :

1.	If 2x2 – 7xy + 3y2 = 0, then the value of x : y is(a) 3 : 2 (b) 2 : 3 (c) 3 : 1 and 1 : 2 (d) 5 : 6
Answer» (c) 3 : 1 and 1 : 2 2x² – 7xy + 3y₂ = 0 ⇒ 2\(\bigg(\frac{x}{y}\bigg)^2\) - 7\(\bigg(\frac{x}{y}\bigg)\) + 3 = 0 ∴ \(\frac{x}{y}\) = \(\frac{-b±\sqrt{b^2-4ac}}{2a}\) = \(\frac{7±\sqrt{49-24}}{4}\) = \(\frac{7±5}{4}\) = 3, \(\frac{1}{2}\) ∴ x : y = 3 : 1 and 1 : 2.

If 2x2 – 7xy + 3y2 = 0, then the value of x : y is(a) 3 : 2 (b) 2 : 3 (c) 3 : 1 and 1 : 2 (d) 5 : 6

Answer»

(c) 3 : 1 and 1 : 2

2x² – 7xy + 3y₂ = 0

⇒ 2\(\bigg(\frac{x}{y}\bigg)^2\) - 7\(\bigg(\frac{x}{y}\bigg)\) + 3 = 0

∴ \(\frac{x}{y}\) = \(\frac{-b±\sqrt{b^2-4ac}}{2a}\) = \(\frac{7±\sqrt{49-24}}{4}\) = \(\frac{7±5}{4}\) = 3, \(\frac{1}{2}\)

∴ x : y = 3 : 1 and 1 : 2.