UPSC CAPF Assistant Commandant Model Paper 4

GIVEN:
[42+27+44+213+48+2x]
FORMULA USED:
(x+y+z)2=x2+y2+z2+2‌xy+2‌yz+2‌zx
CALCULATION:
[42+27+44+213+48+2x]
Changing all the terms into the power of ‘2’:
⇒[24+27+28+213+216+2x]
⇒[24+28+216+27+213+2x]
⇒[24+28+216+2×26+2×212+2×2(x−1)]
Here, the expression inside the bracket will be perfect square of [22+24+28]
And
[22+24+28]2=[(22)2+(24)2+(28)2+2×22×24+
2×24×28+2×22×28]=[24+28+216+2×26+
2×212+2×210]
Comparing this with the given expression:
(x – 1) = 10
⇒ x = 11