Question

please help me in this maths problem​

Answer 1

x = (√3 + 1)/2

x^2 = (√3 + 1)^2 /4

= (3 + 2√3 + 1) /4

= 2(2+√3) /4

= (2 + √3)/2

x^3 = (√3 + 1)^3 /8

= {(√3)^3 + (1)^3 + 3.√3.1 (√3 + 1)} /8

= {3√3 + 1 + 3√3(√3 + 1)} /8

= {3√3 + 1 + 9 + 3√3} /8

= {6√3 + 10} /8

= (3√3 + 5)/4

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

= 4(3√3 + 5)/4 + 2(2 + √3)/2 - 8(√3 + 1)/2 + 7

= 3√3 + 5 + 2 + √3 - 4√3 - 4 + 7

= 4√3 - 4√3 + 14 - 4

= 10 (ans.)