Question

If x – 2y = 3 and xy = 5. find the value of x2 - 4y
${?}^{2}$
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Answer 1

Answer:

6 or - 6

Explanation:

xy = 5 --- (1)

x - 2y = 3 -----(2)

From (1)

xy = 5

⇒ x = $\frac{5}{y}$ ------(3)

SUBSTITUTING EQUATION (3) IN (2) we get,

5/y - 2y =3

⇒ (5 - 2$y^{2}$)y = 3  [by taking LCM]

⇒  5 - 2$y^{2}$ = 3y

⇒ 2$y^{2}$ + 3y - 5 = 0

⇒  2$y^{2}$ + 5y - 2y - 5 = 0

y(2y + 5) - 1(2y + 5) = 0

(y - 1)(2y +5) = 0

∴ y - 1 = 0 or 2y + 5 = 0

⇒ y = 1 or y = -5/2

If we take y = 1 then, by substituting it in equation (3)

x = 5/1 = 5 ------- { STATEMENT 1}

AND If we take y = 5/2 then, by substituting it in equation (3)

x = 5 × 2/5 = 2 ----- {STATEMENT 2}

BY STATEMENT 1,

x2 - 4y = 10 - 4 = 6

By STATEMENT 2,

x2 - 4y = 2×2 - 4×5/2

= 4 - 10

= - 6

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