Question

If $a-b=0.9$ and $ab=0.36$; find $a^2-b^2$ .

• A. $\pm 7.65$
• B. $\pm 1.35$
• C. $\pm 1.5$
• D. $\pm 4.5$

Answer 1

The correct option is B $\pm 1.35$

$a-b=0.9$ and $ab=0.36$
Now, $a-b=0.9$
Squaring both sides, we get
$=>(a-b{)}^2=(0.9{)}^2$
$=>a^2+b^2-2ab=0.81$
$=>a^2+b^2-2\left(0.36\right)=0.81$
$=>a^2+b^2-0.72=0.81$
$=>a^2+b^2=0.81+0.72$
$=>a^2+b^2=1.53$
Now,
$(a^2-b^2{)}^2=(a^2{)}^2+\left(b^2\right)-2a^2{b}^2$
$=>(a^2-b^2{)}^2=(a^2+b^2{)}^2-2a^2{b}^2-2a^2{b}^2$
$=>(a^2-b^2{)}^2=(a^2+b^2{)}^2-4a^2{b}^2$
$=>(a^2-b^2{)}^2=(1.53{)}^2-4(0.36{)}^2$
$=>(a^2-b^2{)}^2=2.3409-0.5184$
$=>(a^2-b^2{)}^2=1.8225$
$=>(a^2-b^2)=\sqrt{1.8225}$
$=>(a^2-b^2)=\pm 1.35$