Question

If x-2y=3 and xy=5 , find the value of x²-4y²​

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Answer 1

Answer:-

x+2y)(x−2y)=3xy

x2−4y2=3xy

x2−3xy−4y2=0

(x−4y)(x+y)=0

This means x - 4y = 0 or x- y = 0

This means x = 4y or x = y

This also could mean that y = x/4.

So the ratio could also be x:y or xx4

x⋅4x

= 4

Answer 2

SOLUTION

दिया गया है:

x - 2y = 3 और xy = 5

सूत्र:

(x - y)^2 = x^2 + y^2 - 2xy

Calculation:

(x - 2y)^2 = x^2 + 4y^2 - 2 × x × 2y

⇒ 32 = x^2 + 4y^2 - 4 × 5

⇒ x^2 + 4y^2 = 9 + 20

⇒ x^2 + 4y^2 = 29 ---- (1)

(x^2 + 4y^2)2 = x^4 + 16y^4 + 2 × x^2 × 4y^2

⇒ 292 = x^4 + 16y^4 + 8 × 25

⇒ x^4 + 16y^4 = 841 - 200

⇒ x^4 + 16y^4 = 641 --- (2)

(x^2 - 4y^2)^2 = x^4 + 16y^4 - 2 × x^2 × 4y^2

⇒ (x^2 - 4y^2)^2 = 641 - 8 × 25

⇒ (x^2 - 4y^2)^2 = 441

⇒ x^2 - 4y^2 = √441

∴ x^2 - 4y^2 = 21