1.

If x2 + xy + y2 = 8 and x + √(xy) + y = 4, then find the value of √(xy)?

Answer» Correct Answer - Option 2 : 1

Given:

x2 + xy + y2 = 8

x + √(xy) + y = 4

Formula used:

(x + y)2 = x2 + y2 + 2xy

(x – y)2 = x2 + y2 – 2xy

Calculation:

∵ x + √(xy) + y = 4

⇒ x + y = 4 – (√xy)

Squaring both sides;

⇒ x2 + y2 + 2xy = 16 + xy – 8√xy

⇒ x2 + y2 + 2xy – xy = 16 – 8√xy

⇒ x2 + y2 + xy = 16 – 8√xy

⇒ 8 = 16 – 8√xy

⇒ 8√xy = 16 – 8

⇒ 8√xy = 8

⇒ √xy = 8/8 = 1


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