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(a-b)^2 Expansion and Visualisation

If a+b=7 an...

Question

If $a + b = 7$ and $a b = 12$ , find the value of $(a^{2} - a b + b^{2})$ .

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Solution

Given $a + b = 7, a b = 12$

$a^{2} - a b + b^{2} = a^{2} + 2 a b + b^{2} - 2 a b - a b$

$= (a + b)^{2} - 3 a b$

$= 7^{2} - 3 \times 12$

$= 49 - 36 = 13$

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