Algebra, please help!

Question

+4

676

2

+185

1. The roots of $7x^2+x-5=0$ are a and b. Compute (a-4)(b-4).

2. The real numbers x and y are such that x + y = 4, x^2 + y^2 = 22, and x^4 = y^4 - 176 sqrt(7). Compute x-y.

Otterstar Jun 26, 2020

Guest · Answer 1 · 2020-06-26T12:29:15

1. (a - 4)(b - 4) = -17.

2. x - y = 12*sqrt(7).

ElectricPavlov · Answer 2 · 2020-06-26T01:29:18

1 . a and b = -1/14 +- sqrt141 / 14 = 0.776739 and −0.919596

(via Quadratic Formula)

so (a-4)(b-4) = 15.857