+0

# need help with algebra

0
127
3

Find 1/(a - 1) + 1/(b - 1) where a and b are the roots of the quadratic equation 2x^2-7x+2 = x^2-11x+1.

Oct 17, 2022

#1
0

1/(a - 1) + 1/(b - 1) = -13/2.

Oct 17, 2022
#2
+2602
0

$${1 \over (a-1)} + {1 \over (b-1)} = {(b-1) \over (a-1)(b-1)} + {(a-1) \over (a-1)(b-1)}$$

$${(b-1) \over (a-1)(b-1)} + {(a-1) \over (a-1)(b-1)} = {a + b -2 \over {ab−a−b+1}}$$

$${a + b -2 \over {ab−a−b+1}} = {a + b -2 \over {ab−(a+b)+1}}$$

$$2x^2-7x+2 = x^2-11x+1$$

$$x^2 + 4x + 1 = 0$$

$$a + b = -{b \over a} = -4$$

$$ab = {c \over a} = 1$$

$${(-4) - 2 \over (1) - (-4) + 1} = {-6 \over 6} = \color{brown}\boxed{-1}$$

.
Oct 17, 2022
#3
0