SSC CGL Model Paper 5

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Question : 54 of 100

Marks: +1, -0

If

x = 4+ √ 13 +√11

, then find

x^4-16x^3+48x^2+128x

572
508
608
576

Solution:

ATQ,

x = 4 + √13 + √11

⇒

x-4 = √13 +√11

Squaring both sides,

(x - 4)^ 2 = ( √13 +√11) ^2

⇒

x^ 2 + 16 - 8x = 13 + 11 +2 √143

⇒

x ^2 - 8x - 8 = 2 √143

Again squaring,

(x ^2 - 8x - 8 )^2 = 4 ×143

⇒

x ^4 + 6 4 x^2 + 64 - 16x^3 + 128x

- 16x^2 = 572

⇒

x ^4 - 16x^3 + 4 8 x^2 + 128x = 508

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