Question

If x = √3 + 1 /2 , find the value of 4x³+2x²-8x+7.

Answer 1

Answer:

x^3 = (√3 + 1)^3/2^3

=> x^3 = (3 + 1 + 9 + 3√3)/8

=> x^3 = (13 + 3√3)/8

x^2 = (√3 + 1)^2/2^2

=> x^2 = (3 + 1 + 2√3)/4

=> x^2 = (4 + 2√3)/4

=> x^2 = (2 + √3)/2

Put the values:

4x^3 + 2x^2 - 8x + 7

=> 4(13 + 3√3)/8 + 2(2 + √3)/2 - 8(√3 + 1)/2 + 7

=> (13 + 3√3)/2 + 2 + √3 - 4√3 - 4 + 7

=> (13 + 3√3 + 4 + 2√3 - 8√3 - 8 + 14)/2

=> (23 - 3√3)/2

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