Given that 2x − 1∶ − 4 = 16x + 1 ∶ 2x − 1 find the possible values of
1 answer:
The possible values of x are 5 and -1/12
<h3>Complete question</h3>Given that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
<h3>How to determine the possible values of x?</h3>The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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We are told that f(x) = x + 2. We want to find .
Squaring f(x) on one side means we square x + 2 on the other.
So,
f(x) = x + 2
(f(x))² = (x + 2)²
= (x + 2)(x + 2)
We can use FOIL to square x + 2. The first terms multiply to x², the outside terms to 2x, the inside terms to 2x and the last terms to 4.
= x² + 2x + 2x + 4
= x² + 4x + 4
So [f(x)]² = x² + 4x + 4