Question

Given a^{2} +b^{2}=256, ab=33
Find (a+b)^2
Find (a-b)^2

Answer 1

Answer :

• value of (a+b)² is 322.
• value of (a-b)² is 190.

Explanation :

a² + b² = 256

ab = 33

(a+b)² = ?

(a-b)² = ?

We know that,

(a+b)² = a² + b² + 2ab

Putting the values,

=> (a+b)² = 256 + (2×33)

=> (a+b)² = 256 + 66

=> (a+b)² = 322

Hence, value of (a+b)² is 322.

___________________

We also know that,

(a-b)² = a² + b² - 2ab

=> (a-b)² = 256 - (2×33)

=> (a+b)² = 256 - 66

=> (a-b)² = 190

Hence, value of (a-b)² is 190.

Answer 2

$\huge \boxed{ \fcolorbox{cyan}{red}{Answer : }}$

Given

Given a^{2} +b^{2}=256, ab=33

Find (a+b)^2

Find (a-b)^2

$\sf{ {a}^{2} + {b}^{2} = 256}$

$\sf{ab = 33}$

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

$\rm{formula}$

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

then

$\rm{(a + {b)}^{2} = 256 + (2 \times 33)}$

$\rm{(a + {b)}^{2} = 256 + 66}$

$\rm{(a + {b)}^{2} = 322}$

$\bf{ \huge{ \boxed{ \red{ \tt{ \green{value \: of \: (a + {b) }^{2} =322 \: }}}}}}$

then

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

$\sf{(a - {b)}^{2} = 256 - (2 \times 33)}$

$\sf{(a - {b)}^{2} = 256 - 33}$

$\sf{(a - {b)}^{2} = 190}$

so...

value of (a-b)² is 190.

Answer

value of (a+b)² is 322.

value of (a-b)² is 190.