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What is the solution of [tex]\((4x - 16)^{\frac{1}{2}} = 36\)[/tex]?

A. [tex]\(x = 5\)[/tex]
B. [tex]\(x = 13\)[/tex]
C. [tex]\(x = 20\)[/tex]
D. [tex]\(x = 328\)[/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the given equation [tex]\((4x - 16)^{1/2} = 36\)[/tex] step by step to find the value of [tex]\(x\)[/tex].

1. Start with the given equation:
[tex]\[ (4x - 16)^{1/2} = 36 \][/tex]

2. To eliminate the square root, square both sides of the equation:
[tex]\[ (4x - 16)^{1/2}^2 = 36^2 \][/tex]
Simplifying this, we get:
[tex]\[ 4x - 16 = 36^2 \][/tex]

3. Calculate [tex]\(36^2\)[/tex]:
[tex]\[ 36^2 = 1296 \][/tex]

4. Substitute this back into the equation:
[tex]\[ 4x - 16 = 1296 \][/tex]

5. To isolate [tex]\(x\)[/tex], add 16 to both sides of the equation:
[tex]\[ 4x - 16 + 16 = 1296 + 16 \][/tex]
Simplifying this, we obtain:
[tex]\[ 4x = 1312 \][/tex]

6. Finally, divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{1312}{4} \][/tex]
Simplifying this, we find:
[tex]\[ x = 328 \][/tex]

So, the solution to the equation [tex]\((4x - 16)^{1/2} = 36\)[/tex] is [tex]\(x = 328\)[/tex]. The correct option is:
[tex]\[ x = 328 \][/tex]
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