Two numbers differ by 9. Four times the bigger exceeds the square of the smaller by 4. Find the larger number

Answer 1

L-S = 9

L= 9+S

4L =S^2 + 4

4(9+S) =S^2 + 4

36 + 4S = S^2 + 4

S^2 -4S - 32 = 0

(S-8)(S+4) = 0

S=8 or -4

L=17 or 5

either 8 and 17, or -4 and 5