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Answer :
Certainly! Let's find the numbers where one is the square of the other and their sum is 182. Here's a step-by-step solution:
1. Define the numbers: Let the first number be [tex]\( x \)[/tex]. Since one number is the square of the other, the second number will be [tex]\( x^2 \)[/tex].
2. Set up the equation: According to the problem, their sum is 182. So we can write the equation:
[tex]\[
x + x^2 = 182
\][/tex]
3. Rearrange the equation: We can rearrange the equation to:
[tex]\[
x^2 + x - 182 = 0
\][/tex]
4. Solve the quadratic equation: We need to find the values of [tex]\( x \)[/tex] that satisfy this equation.
5. Find the roots: The solutions (roots) to this quadratic equation are [tex]\( x = -14 \)[/tex] and [tex]\( x = 13 \)[/tex].
6. Check for valid solutions:
- If [tex]\( x = -14 \)[/tex], then the numbers are [tex]\(-14\)[/tex] and [tex]\((-14)^2 = 196\)[/tex].
- If [tex]\( x = 13 \)[/tex], then the numbers are [tex]\(13\)[/tex] and [tex]\(13^2 = 169\)[/tex].
Both pairs of numbers, [tex]\((-14, 196)\)[/tex] and [tex]\( (13, 169)\)[/tex], satisfy the conditions that one number is the square of the other and their sum is 182.
Thus, the numbers you're looking for are either [tex]\((-14, 196)\)[/tex] or [tex]\( (13, 169)\)[/tex].
1. Define the numbers: Let the first number be [tex]\( x \)[/tex]. Since one number is the square of the other, the second number will be [tex]\( x^2 \)[/tex].
2. Set up the equation: According to the problem, their sum is 182. So we can write the equation:
[tex]\[
x + x^2 = 182
\][/tex]
3. Rearrange the equation: We can rearrange the equation to:
[tex]\[
x^2 + x - 182 = 0
\][/tex]
4. Solve the quadratic equation: We need to find the values of [tex]\( x \)[/tex] that satisfy this equation.
5. Find the roots: The solutions (roots) to this quadratic equation are [tex]\( x = -14 \)[/tex] and [tex]\( x = 13 \)[/tex].
6. Check for valid solutions:
- If [tex]\( x = -14 \)[/tex], then the numbers are [tex]\(-14\)[/tex] and [tex]\((-14)^2 = 196\)[/tex].
- If [tex]\( x = 13 \)[/tex], then the numbers are [tex]\(13\)[/tex] and [tex]\(13^2 = 169\)[/tex].
Both pairs of numbers, [tex]\((-14, 196)\)[/tex] and [tex]\( (13, 169)\)[/tex], satisfy the conditions that one number is the square of the other and their sum is 182.
Thus, the numbers you're looking for are either [tex]\((-14, 196)\)[/tex] or [tex]\( (13, 169)\)[/tex].
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