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(a-b)^2 Expansion and Visualisation

If a - b = ...

Question

If $a - b = 1$ and $a b = 12$ , then $a^{2} + b^{2}$

A

26

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B

28

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C

29

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D

25

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Solution

The correct option is B $25$
Given $a - b = 1$ and $a b = 12$

$(a + b)^{2} = (a - b)^{2} + 4 a b$

$(a + b)^{2} = 1 + 4 (12) = 49$

$a + b = 7$
$a - b = 1$
___________
$2 a = 8$ $\Rightarrow a = 4$

$b = 7 - a$ $\Rightarrow b = 3$

$a^{2} + b^{2} = 4^{2} + 3^{2} = 16 + 9$

$= 25$ .

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Similar questions

a b + b c + c a)

a^{2} + b^{2} + c^{2}

a + b + c

a = 24, b = 26, c = 28

, then the value of

a^{2} + b^{2} + c^{2} - a b - b c - a c

a^{2} + b^{2} = 29

a b = 10

a + b

a^{2} + b^{2} = 29

a b = 10

a - b

a + b + c = 9

a b + b c + c a = 26

, then the value of

a^{2} + b^{2} + c^{2} - 3

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