If x =\sqrt 5 -\sqrt7 , then what is the value of x^ 2 - 24x +_ 8 ?

SSC CPO SI and ASI Model Paper 8

Question : 109 of 200

Marks: +1, -0

x =√ 5 -√7

, then what is the value of

x^ 2 - 24x +_ 8 ?

Solution:

√x = √5 -7

Squaring both sides, we get:

x = 5 +7- 2 √35 = 12-2√ 35

Again squaring both sides, we get:

x^2= 144 +140- 48 √35

=284 -48 √35

Therefore,

x^2 -24x +8

284- 48 √35 -24(12 -2√ 35) +8

=284- 48 √35 -288 + 48 √35 + 8

= – 4 + 8 = 4

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