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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