Question

If a+b=14∧ab=16,then a

2

+b

2

is (a) 124 (b) 132 (c) 164 (d) 196
​

Answer 1

Step-by-step explanation:

Hi !a + b = 10 -------( 1 )ab = 16 -------- --( 2 )Squaring equ.1 , we get :-( a + b )² = 10²a² + 2ab + b² = 100a² + 2 × 16 + b² = 100 a² + b² + 32 = 100a²+ ...

may my answer help u

Answer 2

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

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

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

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

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

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

• 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

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

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