Question

If a +b=14 and ab = 16 then a2+b2?


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Answer 1

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

If a + b = 14 and ab = 16 then find $\sf {a}^{2} + {b}^{2}$ ?

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

$\sf {a}^{2} + {b}^{2} = 164$

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• a + b = 14

• ab = 16

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• $\sf {a}^{2} + {b}^{2}$

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED: }}}}$

$\blue {\sf {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

We know that :

• a + b = 14

Squaring both sides :

$\displaystyle \sf \longrightarrow {(a + b)}^{2} = {(14)}^{2} \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow {a}^{2} + {b}^{2} + 2ab = 196 \: \\ \\ \displaystyle \sf \longrightarrow {a}^{2} + {b}^{2} = 196 - 2ab \:$

Now , we know that :

• ab = 16

Putting value of ab in above equation , we get

$\displaystyle \sf \longrightarrow {a}^{2} + {b}^{2} = 196 - 2(16) \: \\ \\ \displaystyle \sf \longrightarrow {a}^{2} + {b}^{2} = 196 - 32 \: \: \: \: \: \: \\ \\\displaystyle \sf \longrightarrow {a}^{2} + {b}^{2} = 196 - 32 \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow {a}^{2} + {b}^{2} = 164 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue{ \Large\boxed{ \therefore \: \sf {a}^{2} + {b}^{2} = 164 \: }}$