Question

8. If a - b = 0.9 and ab = 0.36; find :
(i) a+b
(ii) a^2-b^2

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{a+b=\pm1.5}}}$

$\green{\tt{\therefore{a^{2}+b^{2}=1.35}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt: \implies a - b = 0.9 \\ \\ \tt: \implies ab = 0.36 \\ \\ \red{\underline \bold{To \: Find : }} \\ \tt: \implies a + b =? \\ \\ \tt: \implies {a}^{2} - {b}^{2} = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies a - b = 0.9 \\ \\ \tt: \implies a = 0.9 + b - - - - - (1) \\ \\ \tt: \implies ab = 0.36 - - - - - (2) \\ \\ \text{Putting \: value \: of \: a \: in \: (2)}\\ \tt: \implies (0.9 + b) \times b = 0.36 \\ \\ \tt: \implies 0.9b + {b}^{2} = 0.36 \\ \\ \tt: \implies 100{b}^{2} + 90b - 36 = 0 \\ \\ \tt: \implies b = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\\tt: \implies b = \frac{ - 90 \pm \sqrt{8100 - 4 \times 100 \times 36} }{2 \times 100} \\ \\ \tt: \implies b = \frac{ - 90 \pm \sqrt{8100 + 14400} }{200} \\ \\ \tt: \implies b = \frac{ - 90 \pm \sqrt{22500} }{200} \\ \\ \tt: \implies b = \frac{ - 90 \pm150}{200} \\ \\ \green{\tt: \implies b = 0.3 \: and \: - 1.2} \\ \\ \text{Putting \: value \: of \: b = 0.3} \\ \\ \tt: \implies a = 0.9+ 0.3 \\ \\ \green{\tt: \implies a = 1.2} \\ \\ \text{Putting \: value \: of \: b = - 1.2} \\ \\ \tt: \implies a = 0.9 + ( - 1.2) \\ \\ \green{\tt: \implies a = - 0.3}$

$\bold{For \: a + b} \\ \tt: \implies a + b =\pm( 1.2 + 0.3) \\ \\ \green{\tt: \implies a + b = \pm1.5} \\ \\ \bold{For \: {a}^{2} - {b}^{2} } \\ \tt: \implies {a}^{2} - {b}^{2} = (({1.2})^{2} - {(0.3})^{2}) \\ \\ \tt: \implies {a}^{2} - {b}^{2} = (1.44 - 0.09) \\ \\ \green{\tt: \implies {a}^{2} - {b}^{2} =1.35}$

Answer 2

$\red{\underline{\underline{\bold{Answer:}}}}$

$\purple{\sf{\therefore{a+b=1.5}}}$

$\purple{\sf{\therefore{a^{2}+b^{2}=1.35}}}$

• Given

➠ a - b = 0.9

➠ ab = 0.36

• To find :

➠ a + b = ?

➠ a^{2} - b^{2} = ?

• According to given question :

$\bold{By \:given \: question} \\ \implies a - b = 0.9 \\ \\ \implies a = 0.9 + b - - - (1)\\ \\ \implies ab = 0.36 - - - (2) \\ \\ {Putting \: value \: of \: a }\\ \implies (0.9 + b) \times b = 0.36 \\ \\\implies 0.9b + {b}^{2} = 0.36 \\ \\ \implies b^{2}+0.9b-0.36=0\\\\ \implies (b-0.3)(b+1.2)=0 \\ \\ \implies b = 0.3 \: and \: - 1.2 \\\\ \implies a =0.9\:and - 0.3$

$\implies a + b \\ \\ \implies ( 1.2 + 0.3)=1.5\\ \\ \bold{For \: another\:question: } \\ \implies {a}^{2} - {b}^{2} \\ \\ \implies (1.2^{2} - 0.3^{2})=(1.44-0.09) \\ \\ \implies {a}^{2} - {b}^{2} =1.35$