Question : If $a + 5b = 13$ and $ab = 9$, then find the value of $a^2 + 25b^2$.
Option 1: 69
Option 2: 79
Option 3: 49
Option 4: 59
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Correct Answer: 79
Solution :
Given: $ab = 9$
$a + 5b = 13$
$⇒(a + 5b)^2 = 13^2$
$⇒a^2 + 25b^2 + 10ab = 169$
$⇒a^2 + 25b^2 +10×9 = 169$
$⇒a^2 + 25b^2 = 169-90=79$
Hence, the correct answer is 79.
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