Question

If a +b = 6 and ab = 8, evaluate (i) a2 + b2 and (ii) a - b.​

Answer 1

Step-by-step explanation:

{a+b}^2 = a^2+b^2+2ab

36 -16 = a^2+b^2

= 20

{a-b}^2 = 20 -16

a-b = 4

Answer 2

Step-by-step explanation:

Given:-

a+b=6

ab=8

To find:-

${\textcircled {\textsf {1}}}a^2+b^2$

${\textcircled {\textsf {2}}}a-b$

Solution:-1

• a+b=6
• ab=8

$\\\qquad\quad\sf {:}\longrightarrow a+b=6$

$\\\qquad\quad\sf {:}\longrightarrow (a+b)^2=6^2$

$\\\qquad\quad\sf {:}\longrightarrow a^2+b^2+2ab=36$

• Substitute the value of ab

$\\\qquad\quad\sf {:}\longrightarrow a^2+b^2+2 (8)=36$

$\\\qquad\quad\sf {:}\longrightarrow a^2+b^2+16=36$

$\\\qquad\quad\sf {:}\longrightarrow a^2+b^2=36-16$

$\\\qquad\quad\bf {:}\longrightarrow a^2+b^2=20$

$\rule {220}{1}$

Solution-2:-

$\\\qquad\quad\sf {:}\longrightarrow a-b$

$\\\qquad\quad\sf {:}\longrightarrow (a-b)^2$

$\\\qquad\quad\sf {:}\longrightarrow a^2+b^2-2ab$

$\\\qquad\quad\sf {:}\longrightarrow 20-2 (8)$

$\\\qquad\quad\sf {:}\longrightarrow (a-b)^2=20-16$

$\\\qquad\quad\sf {:}\longrightarrow (a-b)^2=4$

$\\\qquad\quad\sf {:}\longrightarrow a-b=\sqrt {4}$

$\\\qquad\quad\bf {:}\longrightarrow a-b=2$