Question

If a+b=7 and ab=10, find (a²+b²)

Answer 1

Answer:

QUESTION:

If a+b=7 and ab=10, find (a²+b²)

Given:

a+b=7

ab=10

R.T.F:

(a²+b²)

SOLVATION:

$(a + b) {}^{2} = a {}^{2} + 2ab + b {}^{2} \\ \: \: \: (7) {}^{2} \: \: \: = a {}^{2} + b {}^{2} + 2(10) \\ \: \: \:49 \: \: \: \: \: = a {}^{2} + b {}^{2} + 20 \\ a {}^{2} + b {}^{2} = 49 - 20 \\ a {}^{2} + b {}^{2} = 29$

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Answer 2

Answer:

$(a + b) {}^{2} = {a}^{2} + {b}^{2} = 2ab \\ {a}^{2} + {b}^{2} = (a + b) {}^{2} - 2ab \\ = (7) {}^{2} - 2(10) \\ = 49 - 20 \\ {a}^{2} + {b }^{2} = 29.$

Step-by-step explanation:

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