Choose the correct value for the value of x (\sqrt5-\sqrt10)^2+(\sqrt2+5)^2=x^2-22

Simplification Test 1

Question : 22 of 40

Marks: +1, -0

Choose the correct value for the value of x

(√5-√10)^2+(√2+5)^2=x^2-22

Solution:

x^2-22=(√5-√10)^2+(√2+5)^2

(a-b)^2=a^2+b^2-2ab

(a+b)^2=a^2+b^2+2ab

x^2-22=(√5)^2+(√10)^2-2√5√10+(√2)^2+(5)^2+10√2

x^2=5+10-2√50+2+25+10√2+22

x^2=5+10-10√2+2+25+10√2+22

x^2=64

⇒x=8

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