Question : If $a+b=10$ and $a^2+b^2=58$, find the value of $ab$
Option 1: 24
Option 2: 27
Option 3: 30
Option 4: 21
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Correct Answer: 21
Solution :
Given: $a+b=10$ and $a^2+b^2=58$
To find: $ab$
$a+b=10$
Squaring both sides, we get:
$(a+b)^2=10^2$
⇒ $a^2+b^2+2ab=100$
Putting the values, we get:
⇒ $58+2ab=100$
⇒ $2ab=100-58$
⇒ $2ab=42$
⇒ $ab=21$
Hence, the correct answer is 21.
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