/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 92 Find all values of \(x\) satisfy... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 92

Find all values of \(x\) satisfying the given conditions. $$y=(x-5)^{\frac{3}{2}} \text { and } y=125$$

Short Answer

Expert verified
The value of \( x \) that satisfies both equations is 10.

Step by step solution

01

Equate the two equations

Since \( y \) is common in both equations, equate them to each other: \[ (x-5)^{\frac{3}{2}} = 125 \]
02

Solve for \( x \)

First, take cube root on both sides of the equation which gets rid of the fractional exponent:\[ (x-5) = \sqrt[3]{125} \]We know that \(\sqrt[3]{125}\) is 5, so simplify it to get:\[ x-5 = 5 \]
03

Find the value of \( x \)

Finally, solve for \( x \) by adding 5 to both sides: \[ x = 5+5 = 10 \]

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Most popular questions from this chapter

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