Given, $a = - 2$ and $b = 5$ , which of the following expressions has the least value.

2 a + 3 b

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a^{2} - b^{2}

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a - b

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2 b - a

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Solution

The correct option is B $a^{2} - b^{2}$
$2 a + 3 b = 2 (- 2) + 3 (5) = - 4 + 15 = 11$
$a^{2} - b^{2} = (- 2)^{2} - (5)^{2} = 4 - 25 = - 21$
$a - b = - 2 - 5 = - 7$
$2 b - a = 2 (5) - (- 2) = 10 + 4 = 14$
Clearly, value of $a^{2} - b^{2}$ is least among them.
Option B is correct.

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Similar questions

\frac{a^{2} + 2 a b + b^{2}}{a^{2} - b^{2}} = 2 a + 2 b

a - b

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a^{2} + b^{2} = 5

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(\frac{a + 3 b}{(a - b)^{2}} + \frac{a - 3 b}{a^{2} - b^{2}}) : \frac{a^{2} + 3 b^{2}}{(a - b)^{2}}

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