Asked by Amraj Sahota on Mar 10, 2024

Verified

For $f(x)=x −x−169 $ , find x such that $f(x)=1$ .

A) 14,450

B) 14,112

C) 28,900

D) 7,056

E) $7,225$

A) 14,450

B) 14,112

C) 28,900

D) 7,056

E) $7,225$

Solve

To find the answer or solution to a mathematical problem or equation.

Expression

A combination of symbols, numbers, and operation signs that represents a quantity but does not include an equality sign.

- Strengthen capability in analyzing equations with radicals and fathoming the concept of irrelevant solutions.

Verified Answer

DT

Destiny tillman

Mar 10, 2024

Final Answer :

E

Explanation :

To solve $f(x)=1$ , we set $x −x−169 =1$ . Squaring both sides gives $x−2x(x−169) +x−169=1$ , simplifying to $2x−170=2x(x−169) $ . Dividing by 2 and squaring again yields $(x−85)_{2}=x(x−169)$ . Expanding and simplifying gives a quadratic equation in $x$ , which, when solved, leads to $x=7225$ as the solution that makes sense in the context of the original equation, since it must be greater than 169 to keep the square root of $x−169$ real.

## Learning Objectives

- Strengthen capability in analyzing equations with radicals and fathoming the concept of irrelevant solutions.