Question

if
$a + b = 4$
and
$ab = 4$
then
${a}^{2} - ab + {b}^{2}$
and
${a}^{2} + ab + {b}^{2}$
​

Answer 1

Answer:

Formula (a−b)

2

=a

2

+b

2

−2ab

Given, a

2

+b

2

=41 and ab=4

So, (a−b)

2

=a

2

+b

2

−2ab=41−2×4=41−8=33

=>a−b=

33

Answer 2

ANSWER:

Given:

• a + b = 4
• ab = 4

To Find:

• Values of a^2 - ab + b^2 and a^2 + ab + b^2

Solution:

$\text{We know that} \\\\:\longrightarrow \sf{a^2 + b^2 = (a + b)^2 - 2ab} \\\\\text{\bf{1) a ^2 - ab + b ^2 }} \\\\:\implies \sf{a^2 + b^2 - ab} \\\\:\implies\sf{[(a + b)^2 - 2ab] - ab} \\\\:\implies \sf{(a + b)^2 - 3ab} \\\\:\implies \sf{(4)^2 - 3(4)} \\\\:\implies \sf{16 - 12} \\\\:\implies \bf{4} \\\\\text{\bf{2) a ^2 + ab + b ^2 }} \\\\:\implies \sf{a^2 + b^2 + ab} \\\\:\implies\sf{[(a + b)^2 - 2ab] + ab} \\\\:\implies \sf{(a + b)^2 - ab} \\\\:\implies \sf{(4)^2 - (4)} \\\\:\implies \sf{16 - 4} \\\\:\implies \bf{12}$

Formula used:

• a^2 + b^2 = (a + b)^2 - 2ab

Learn More:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identities}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\bf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\bf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\8)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\9)\bf\: A^{3} - B^{3} = (A-B)(A^{2} + AB + B^{2})\\\\ \end{minipage}}$