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If (73)2 is subtracted from the square of a number, the answer so obtained is 5075. What is the number ?
Answer & Solution
Correct Answer:
Option
C
Let the number be x
Then,
$$\eqalign{ & \Leftrightarrow {x^2} - {\left( {73} \right)^2} = 5075 \cr & \Leftrightarrow {x^2} - 5329 = 5075 \cr & \Leftrightarrow {x^2} = 5075 + 5329 \cr & \Leftrightarrow {x^2} = 10404 \cr & \Leftrightarrow x = \sqrt {10404} \cr & \Leftrightarrow x = 102 \cr} $$
Then,
$$\eqalign{ & \Leftrightarrow {x^2} - {\left( {73} \right)^2} = 5075 \cr & \Leftrightarrow {x^2} - 5329 = 5075 \cr & \Leftrightarrow {x^2} = 5075 + 5329 \cr & \Leftrightarrow {x^2} = 10404 \cr & \Leftrightarrow x = \sqrt {10404} \cr & \Leftrightarrow x = 102 \cr} $$
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