If 3+√7 / 3-√7 = a+b√7 find a and b
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Answered by
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
------- -------------------- ------------------------ = -----------------= -------------= -------+ ----
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
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
do u have rd sharma? check it out pg no 3.7 example 11 no.(ii)
no I don't have it
a step is not visible in the answer
which i typed
which step
1st row after last step i.e after 16/2 there should be root 7/2
+root 7/2
I didn't understand the answer
Answered by
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
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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