Question

If X=1/(2-√3).prove that x^3-2x^2-7x+5=3

Answer 1

SOLUTION

GIVEN,

x= 1/(2-√3)

=) 1/2-√3)×(2+√3)/(2+√3)

=) (2+√3)/(4-3)

=) (2+√3)

Now,

L.H.S.=x^3-2x^2-7x+5

=) (2+√3)^3-2(2+√3)^2-7(2+√3)+5

=)2^3+(√3)^3+3(4)(√3)+3(2)(3)-2[4+3+4√3]-14-7√3+5

=) 8+3√3+12√3+18-8-6-8√3-14-7√3+5

=) 8+18-8-6-14+5+3√3+12√3-8√3-7√3

=) 3+15√3-15√3

=) 3 [Proved]✓

LHS= RHS.

Hope it helps

Answer 2

Step-by-step explanation:

plzz refer to the attached file...

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