If (2 a+\frac{3}{a}-1)=11, what is the value of (4 a^{2}+\frac{9}{a^{2}}) ?

SSC CGL 20 Aug 2021 Shift 1 Paper

Question : 59 of 100

Marks: +1, -0

(2 a+\;{3}/{a}-1)=11

, what is the value of

(4 a^{2}+\;{9}/{a^{2}})

Solution:

\;\text " (c) Given, "\;(2 a+\;{3}/{a}-1)=11

⇒ \;\; 2 a+\;{3}/{a}=11+1=12

Squaring on both sides,

⇒ \;\; (2 a+\;{3}/{a})^{2}=(12)^{2}

⇒ 4 a^{2}+\;{9}/{a^{2}}+2 × 2 a × \;{3}/{a}=144

⇒ \;\; 4 a^{2}+\;{9}/{a^{2}}=144-12

∴ \;\; 4 a^{2}+\;{9}/{a^{2}}=132 .

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