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The sum of two numbers is 25 and their difference is 13. Find their product :
Answer & Solution
Correct Answer:
Option
B
Let the numbers be x and y
Then,
x + y = 25 and x - y = 13
$$\eqalign{ & \Leftrightarrow 4xy = {\left( {x + y} \right)^2} - {\left( {x - y} \right)^2} \cr & \Leftrightarrow 4xy = {\left( {25} \right)^2} - {\left( {13} \right)^2} \cr & \Leftrightarrow 4xy = 625 - 169 \cr & \Leftrightarrow 4xy = 456 \cr & \Leftrightarrow xy = 114 \cr} $$
Then,
x + y = 25 and x - y = 13
$$\eqalign{ & \Leftrightarrow 4xy = {\left( {x + y} \right)^2} - {\left( {x - y} \right)^2} \cr & \Leftrightarrow 4xy = {\left( {25} \right)^2} - {\left( {13} \right)^2} \cr & \Leftrightarrow 4xy = 625 - 169 \cr & \Leftrightarrow 4xy = 456 \cr & \Leftrightarrow xy = 114 \cr} $$
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