Question

hey

answer it plzzzzzzzxx​

Answer 1

# Question :

$\tt If \: 3 + \frac{ ({7})^{ \frac{1}{2} } }{3} - ( {7})^{ \frac{1}{2} } = a + b {(7)}^{ \frac{1}{2} } \: then \: (a,b) \: is$

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

$\green{\tt{\therefore{Value\:of\:(a,b)=(3,\frac{-2}{3})}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies 3 + \frac{ {(7)}^{ \frac{1}{2} } }{3} - {(7)}^{ \frac{1}{2} } = a + b {(7)}^{ \frac{1}{2} } \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Value \: of \: (a,b)=?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies 3 + \frac{ {(7)}^{ \frac{1}{2} } }{3} - {(7)}^{ \frac{1}{2} } = a + b {(7)}^{ \frac{1}{2} } \\ \\ \tt: \implies 3 + \frac{ \sqrt{7} }{3} - \sqrt{7} = a + b \sqrt{7} \\ \\ \text{Taking \: lcm : }\\ \tt: \implies \frac{3 \times 3 + \sqrt{7} - 3 \times \sqrt{7} }{3} = a + b \sqrt{7} \\ \\ \tt: \implies \frac{9 + \sqrt{7} - 3 \sqrt{7} }{3} = a + b \sqrt{7} \\ \\ \tt: \implies \frac{9 - 2 \sqrt{7} }{3} = a + b \sqrt{7} \\ \\ \tt: \implies \frac{9}{3} + ( \frac{ - 2 \sqrt{7} }{3} ) = a + b \sqrt{7} \\ \\ \tt: \implies 3 + ( \frac{ - 2 \sqrt{7} }{3} ) = a + b \sqrt{7} \\ \\ \text{On \: comparing \: both \: sides : } \\ \green{\tt: \implies a = 3} \\ \\ \tt: \implies b \sqrt{7} = \frac{ - 2 \sqrt{7} }{3} \\ \\ \tt: \implies b = \frac{ - 2 \sqrt{7} }{3 \sqrt{7} } \\ \\ \green{\tt: \implies b = \frac{ - 2}{3} }$

Answer 2

$<marquee Scrollamount =1300 > I hope it's helps you</marquee >$