Asked by Amraj Sahota on Mar 10, 2024

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For f(x) =x−x−169f ( x ) = \sqrt { x } - \sqrt { x - 169 }f(x) =xx169 , find x such that f(x) =1f ( x ) = 1f(x) =1 .

A) 14,450
B) 14,112
C) 28,900
D) 7,056
E) 7,2257,2257,225

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.
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Verified Answer

DT
Destiny tillman

Mar 10, 2024

Final Answer :
E
Explanation :
To solve f(x)=1f(x) = 1f(x)=1 , we set x−x−169=1\sqrt{x} - \sqrt{x - 169} = 1xx169=1 . Squaring both sides gives x−2x(x−169)+x−169=1x - 2\sqrt{x(x - 169)} + x - 169 = 1x2x(x169)+x169=1 , simplifying to 2x−170=2x(x−169)2x - 170 = 2\sqrt{x(x - 169)}2x170=2x(x169) . Dividing by 2 and squaring again yields (x−85)2=x(x−169)(x - 85)^2 = x(x - 169)(x85)2=x(x169) . Expanding and simplifying gives a quadratic equation in xxx , which, when solved, leads to x=7225x = 7225x=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−169x - 169x169 real.