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Applied Course | Mock GATE | Test 1 | Question: 7

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$P=\sqrt{20+\sqrt{20+\sqrt{20+ \sqrt{20+ \dots + \infty}}}}$
Sqaring on both sides
$P^2=20+\sqrt{20+\sqrt{20+ \sqrt{20+ \dots + \infty}}}$
$P^2=20+P$
$P^2-P-20=0$
$P^2 +4P-5P-20=0$
$P(P+4) - 5(P+4)=0$
$(P-5)(P+4)=0$
$P=5$
$P=-4$
Ignore the negative value so $P=5$
$\text{Trick}$
$P=\sqrt{20+\sqrt{20+\sqrt{20+ \sqrt{20+ \dots + \infty}}}}$
Make factors here $20 = 4 \times 5$
If sign $'+'$ take answer as highest factor (i.e) 5.
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