Question

If ab=6and a+b=5the the value of (a^2+b^2)is

Answer 1

Answer:

$13

Step-by-step explanation:

The expression, ${a^2} + {b^2}$occurs in the expansion of the formula ${\left( {a + b} \right)^2}$, so we will use this expansion to find out the value of the required expression.

${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}$ …equation (1)

On rearranging the terms in equation (1), we obtain,

${a^2} + {b^2} = {\left( {a + b} \right)^2} - 2ab$ …equation (2)

We now substitute the values of a + b and ab in equation (2), we get,

${a^2} + {b^2} = {\left( 5 \right)^2} - 2\left( 6 \right) \Rightarrow {a^2} + {b^2} = 25 - 12 = $13

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