If a+b=p, a b=q, then (a^{4}+b^{4}) is equal to

Correct Answer is : p4−4p2q+2q2

SSC CHSL 4 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 72 of 100

Marks: +1, -0

a+b=p, a b=q

, then

(a^{4}+b^{4})

is equal to

Solution:

Given,

(a+b)=p

and

a b=q

Taking square on both sides,

∴ (a+b)^{2}=a^{2}+b^{2}+2 a b

⇒ \;\; p^{2}=a^{2}+b^{2}+2 q

⇒ \;\; a^{2}+b^{2}=p^{2}-2 q

Taking square again on both side,

(a^{2}+b^{2})^{2}=a^{4}+b^{4}+2 a^{2} b^{2}

∴ a^{4}+b^{4}=(p^{2}-2 q)^{2}-2(q)^{2}

∴ a^{4}+b^{4}=p^{4}+4 q^{2}-2 × p^{2} × 2 q-2 q^{2}

∴ a^{4}+b^{4}=p^{4}-4 p^{2} q+2 q^{2}

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