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Question : 11 of 160
Marks:
+1,
-0
Solution:
We have,
√‌+√‌=‌ Let
‌‌√‌=y Then,
‌‌y+‌=‌⇒‌=‌ ⇒‌‌10y2+10=29y ⇒‌‌10y2−29y+10=0 ⇒‌‌10y2−25y−4y+10=0 ⇒‌‌5y(2y−5)−2(2y−5)=0 ⇒‌‌(5y−2)(2y−5)=0 ⇒‌‌y=‌,‌ Now, if
y=‌⇒√‌=‌ ⇒‌‌‌=‌ ⇒‌‌125x=4x−8 ⇒ 121x=−8 ⇒‌‌x=−8∕121 And if
y=‌⇒√‌=‌ ⇒‌‌‌=‌ ⇒‌‌‌=‌⇒5x−10=4x ⇒‌‌x=10 ∴ Let
α=10 and
β=‌ ∴‌‌√α2−114β2 (∵α>β) =√(10)2−114(‌)2 =√100−64 =√36=6
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