Question

Carilah nilai (x1 + x2) dan (x1 . x2) apabila x1 dan x2 merupakan akar akar persamaan eksponensial dibawah ini
a. 11^x2 + 3x +2 = 121^x2 - 3x + 2
b. 5^x2 -3x + 2 + 5^x2 - 3x + 1 = 30
c. 5^x2 + 2x + 5 = 5^-3x - 1

Answer 1

A.
11^(x² + 3x+ 2) = 121^(x² - 3x + 2)
11^(x² + 3x + 2) = 11^{2(x²-3x+2)}
x² + 3x + 2 = 2x² - 6x + 4
x² -2x² +3x + 6x + 2 - 4 = 0
- x² + 9x - 2 = 0
a = -1, b = 9 , c = - 2
x₁ + x₂  = -b/a = -(9)/(-1) = 9/1 = 9
x₁.x₂ = c/a = (-2)/(-1) = 2/1 =2

b.
5^(x²-3x+2) + 5^(x²-3x +1) = 30
5^(x²-3x).5^2 + 5^(x²-3x). 5^1 = 30
25. 5^(x²-3x) + 5 . 5^(x²-3x) = 30 .
(25+5) .5^(x²-3x) = 30
(30). 5^(x²-3x) =  30
5^(x²-3x) = 1 = 5^0
x²-3x = 0
a = 1 , b = -3 , c = 0
x₁+x₂ = -b/a = -(-3)/(1) = 3
x₁. x₂ = c/a = 0/1 = 0

3.
5^(x²+2x+5)= 5^(-3x-1)
x² + 2x + 5 = -3x -1
x² + 2x + 3x + 5 + 1= 0
x² + 5x + 6 = 0
a= 1, b = 5 , c = 6
x₁+x₂ = -b/a = -(5)/6 = -5/6
x₁.x₂ = c/a = 6/1 = 6
..