Algebra problem

Question

If c² - c= 21, find (c+4)²+1/(c+4)²

Answer 1

This is a quadratic equation c² - c = 21, or c² -c - 21 = 0, solve for c

Δ = b² - 4ac = ( -1)² - 4(1)(-21) = 85 > 0 therefore you have two roots

c = - b ± √Δ / 2a = -(-1) ± √85 / 2(1) = 1 ± 9.22 / 2

c1 = 1+9.22/2 = 10.22 / 2 = 5.11, and c2 = 1- 9.22/ 2 = -8.22 / 2 = - 4.11 and,

(c+4)²+1/(c+4)² compute ( c+4)² = ( 5.11 + 4)² = 83

and (c+4)²+1/(c+4)² = 83 + 1/83 = 83 + 0.012 = 83.012

or (c+4)²+1/(c+4)² compute (c²+4)² = ( -4.11 + 4)² = 0.012

and (c+4)²+1/(c+4)² = 0.012 + 1/0.012 = 0.012+ 83.333 = 83.345