Question

If a+b = 10 and ab=2, find the value of
a) a^2+b²
b)(a-b)^2

give full solution.​

Answer 1

Question

If a+b = 10 and ab=2, find the value of

a) a^2+b²

b)(a-b)^2

Solution

Given :-

• a + b = 10 -----------(1)
• ab = 2 -------------(2)

Find :-

• Value of a² + b²
• Value of (a-b)²

Explanation

Important Formula

★ ( a + b )² = a² + b² + 2ab

★ ( a-b)² = (a+b)² - 4ab

So,

Squaring both side of equ(1)

==> (a + b)² = 10²

==> a² + b² + 2ab = 100

keep Value of equ(2)

==> a² + b² = 100 - 2* 2

==> a² + b² = 100 - 4

==> a² + b² = 96

_____________________

Again,

==> ( a-b)² = (a+b)² - 4ab

Keep Value by equ(1) & (2)

==> (a-b)² = (10)² - 4*2

==> (a-b)² = 100 - 8

==> (a - b)² = 92

_______________________

Hence

• Value of a² + b² = 96
• Value of (a-b)² = 92

_______________

Answer 2

Solution :

$\bf{\underline{\underline{\bf{Given\::}}}}}$

If a + b = 10 & ab = 2.

$\bf{\underline{\underline{\bf{To\:find\::}}}}}$

The value of :

• a² + b²
• (a - b)²

$\bf{\underline{\underline{\bf{Explanation\::}}}}}$

Formula :

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

A/q

$\dashrightarrow\tt{a^{2}+b^{2} =(10)^{2} -2(2)}\\\\\dashrightarrow\tt{a^{2}+b^{2}=100-4}\\\\\dashrightarrow\tt{\pink{a^{2}+b^{2}=96}}$

&

Formula :

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

$\dashrightarrow\tt{(a-b)^{2} =(a+b)^{2} -2ab-2ab}\\\\\dashrightarrow\tt{(a-b)^{2} =(10)^{2} -2(2)-2(2)}\\\\\dashrightarrow\tt{(a-b)^{2} =100-4-4}\\\\\dashrightarrow\tt{(a-b)^{2} =100-8}\\\\\dashrightarrow\tt{\pink{(a-b)^{2} =92}}$