Question

Help me

It's urgent yr.......xD​

Answer 1

Ye le vhai chap daala maine....

3+√7 / 3-√7

multiply 3+√7 on both numerator and denomerator

(3+√7)² / (3-√7)(3+√7) = a+b√7

⇒9 + 7 + 6√7 / 3² -√7² = a+b√7

⇒16+ 6√7 / 9-7 =a+b√7

⇒16+ 6√7 / 2 =a+b√7

⇒2(8+3√7)/2 =a+b√7

⇒8 +3√7 =a+b√7

on compairing both sides

a=8

b=3

Answer 2

Aɴꜱᴡᴇʀ

$\huge \tt \blue{a = 8} \\ \\ \huge \tt \blue{b = 3}$

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Gɪᴠᴇɴ

$\large \tt \frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

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ᴛᴏ ꜰɪɴᴅ

The valur of "a" and "b"

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Sᴛᴇᴘꜱ

Let's rationalise the denominator to find our answer

Note:-

• Multiply the number with its opposite sign

So ,

$\large \tt \frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } \\ \\ \large \tt{} \frac{9 + 3 \sqrt{7 } + 3 \sqrt{7} + 7 }{9 - 7} \\ \\ \large \tt{} \frac{16 + 6 \sqrt{7} }{2} \\ \\ \large \tt here \: 2 \: is \: common \: for \: both \: so \\ \\ \large \tt{} \frac{ \cancel{16}}{ \cancel2} + \frac{ \cancel6 \sqrt{7} }{ \cancel2} \\ \\ \large \tt{} \pink{\dashrightarrow{}8 +3 \sqrt{7} } \\ \\ \large \tt{}thus \: the \: value \: of \: \green{a = 8} \: and \: \orange{b = 3}$

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$\huge{\mathfrak{\purple{hope\; it \;helps}}}$