Math, asked by SandeshG, 1 year ago

If 3+√7 / 3-√7 = a+b√7 find a and b

Answers

Answered by vinosharubalitanu

199

3+√7 × 3+√7 =[3+√7]² = 3²+2×3×√7+(√7)² 9+6√7+7 16+6√7 16 √7
------- -------------------- ------------------------ = -----------------= -------------= -------+ ----
3-√7 × 3+√7 =3²-(√7)² = 9-7 2 2 2 2
= 8+3√7
a+b√7
a=8;b=3

SandeshG: Maybe a=7 b=1

vinosharubalitanu: i edited the ans. first which i did was wrong i.e. the last step.now it is correct.this sum is in rd sharma book

vinosharubalitanu: do u have rd sharma? check it out pg no 3.7 example 11 no.(ii)

SandeshG: no I don't have it

vinosharubalitanu: a step is not visible in the answer

vinosharubalitanu: which i typed

SandeshG: which step

vinosharubalitanu: 1st row after last step i.e after 16/2 there should be root 7/2

vinosharubalitanu: +root 7/2

SandeshG: I didn't understand the answer

Answered by jaijoshi

556

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

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