Question

If a²- b²= 132 and a+b = 22, then find the value of a+b².

Answer 1

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

${\bf{\green{Given,}}}$

${\bf{\red{a^2-b^2=132}}}$

${\bf{\blue{a+b=22....EQ1}}}$

${\bf{\green{WKT,}}}$

${\bf{\pink{=>a^2-b^2=(a+b)(a-b)}}}$

${\bf{\blue{=>(132)=(22)(a-b)}}}$

${\bf{\blue{=>a-b=132/22}}}$

${\bf{\blue{=>a-b=6....EQ2}}}$

${\bf{\orange{=>EQ2-EQ1}}}$

${\bf{\green{=>a-b-a-b=6-22}}}$

${\bf{\green{=>-2b=-16}}}$

${\bf{\green{=>b=8}}}$

${\bf{\red{sub,b=8 in EQ1}}}$

${\bf{\blue{=>a+8=22}}}$

${\bf{\blue{=>a=22-8}}}$

${\bf{\blue{=>a=14}}}$

${\bf{\pink{Now,}}}$

${\bf{\green{=>a+b^2}}}$

${\bf{\green{=>14+8^2}}}$

${\bf{\green{=>14+64}}}$

${\bf{\orange{=>78}}}$

Answer 2

Answer:

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