Given (5x + 1) / [(x-1) (X-2)] = A / (x-1) + B / (X-2), find the value of a-b

Given (5x + 1) / [(x-1) (X-2)] = A / (x-1) + B / (X-2), find the value of a-b

Multiply by (x-1) (X-2)
5x+1=A(x-2)+B(x-1)
5x+1=(A+B)x+(-2A-B)
So 5 = a + B
1=-2A-B
So a = - 6
B=11
So A-B = - 17

Given x = 1 / (2 - √ 5), find the value of X + 3x-5x + 1

x=1/(2-√5) x=(2+√5)/(2-√5)(2+√5) x=-2-√5 x^3+3x^2-5x+1 =x^3+3x^2-4x-x+1 =x(x^2+3x-4)-(x-1) =x(x-1)(x+4)-(x-1) =(x-1)(x^2+4x-1) =(x-1)(x^2+4x+4-5) =(x-1)[(x+2)^2-5] =(x-1)[(-2-√5+2)^2-5] =(x-1)[(...

X = (√ 5-1) / 2, find the value of x ^ 5-5x
X = (√ 5 - 1) / 2, find the value of x ^ 5 - 5x

2x+1=√5
4x²+4x+1=5
x²=-x+1
So x ^ 4 = (- x + 1) & sup2;
=x²-2x+1
=-x+1-2x+1
=-3x+2
x^5=x×x^4
=x(-3x+2)
=-3x²+2x
=-3(-x+1)+2x
=5x-3
So x ^ 5-5x
=5x-3-5x
=-3