Answer:
-3.5 or -6
Step-by-step explanation:
2x^2+19x+40=-2
2x^2+19x+40+2=0
2x^2+19x+42=0
2x^2+(12+7)x+42=0
2x^2+12x+7x+42=0
2x(x+6)+7(x+6)=0
(x+6)(2x+7)=0
either,
x+6=0
x=-6
or,
2x+7=0
2x=-7
x=-7/2
x=-3.5
Step-by-step explanation:
-26a-19-35=-84
-26a-19+(19)-35=-84+(19)
-26a-35=-65
-26a-35+(35)=-65+(35)
-26a=-30
-26a/26=-30/26
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
