Question

if a+b=7 and ab=12 evaluate a²+b²​

Answer 1

ANSWER:25

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Answer 2

Given

$\bf \large \implies \: \: a \: + \: b \: = \: 7$

$\bf \large \implies \: \: a \: \times \: b \: = \: 12$

Using Identity

$\bf \large \rightarrow \: \: ( \: a \: + \: b) ^{2} = \: {a }^{2} \: + \: 2ab \: + \: {b}^{2}$

Substuting the values

$\bf \large \rightarrow \: \: ( \: a \: + \: b) ^{2} = \: {a }^{2} \: + \: 2 \: \times \: ab \: + \: {b}^{2}$

$\bf \large \rightarrow \: \: ( 7) ^{2} = \: {a }^{2} \: + \: 2 \: \times \: 12 \: + \: {b}^{2}$

$\bf \large \rightarrow \: \: 49 = \: {a }^{2} \: + 24 + \: {b}^{2}$

$\bf \large \rightarrow \: \: 49 \: - \: 24 \: = \: {a }^{2} \: + \: {b}^{2}$

$\bf \large \rightarrow \: \: 25 \: = \: {a }^{2} \: + \: {b}^{2}$

Hence , the value of a² + b² is 25.