SSC CGL 20 Aug 2021 Shift 2 Paper

Question : 60 of 100

Marks: +1, -0

\left(56 \sqrt{7} x^{3}-2 \sqrt{2} y^{3}\right) \div(2 \sqrt{7} x-\sqrt{2} y)

=A x^{2}+B y^{2}-C x y

, then find the value of

A+B-\sqrt{14} C

Solution:

Given,

(56 √{7} x^{3}-2 √{2} y^{3}) ÷(2 √{7} x-√{2} y)

=A x^{2}+B y^{2}-C x y

We know that,

a^{3}-b^{3}=(a-b)(a^{2}+b^{2}+a b)

\;\text " By LHS, "\; \;{(2 √{7} x)^{3}-(√{2} y)^{3}}/{(2 √{7} x-√{2} y)}

⇒ \;{(2 √{7} x-√{2} y)(28 x^{2}+2 y^{2}+2 √{14 x y})}/{[(2 √{7} x)-√{2} y]}

By comparing both sides we get,

A=28, B=2

C=-2 √{14}

∴ A+B-C √{14}

=28+2-(-2 √{14}) √{14}

=30+2 × 14

=30+28=58

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