Question : If $a-b=11$ and $ab=24$, then the value of $(a^2+b^2)$ is:
Option 1: 169
Option 2: 37
Option 3: 73
Option 4: 48
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Correct Answer: 169
Solution :
Given: $a-b = 11$ and $ab = 24$
Squaring both sides of the equation: $a-b = 11$, we get,
$⇒(11)^{2} = a^{2}+b^{2}-2×ab$
Substituting the value of $ab$ in the above equation and get,
$⇒121 = a^{2}+b^{2}-48$
$\therefore a^{2}+b^{2} = 169$
Hence, the correct answer is 169.
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