Find the values of a and b if: 3+V2 = a + b12 3-12
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Answered by
1
Answer:
a = 2 and b = -1
Step-by-step explanation:
Given: \frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}
3
+1
3
−1
=a+b
3
To find: vale of a & b
We find value of a & b by rationalizing the denominator of LHS and then equating with RHS
Consider,
LHS
=\frac{\sqrt{3}-1}{\sqrt{3}+1}=
3
+1
3
−1
=\frac{\sqrt{3}-1}{\sqrt{3}+1}\times\frac{\sqrt{3}-1}{\sqrt{3}-1}=
3
+1
3
−1
×
3
−1
3
−1
=\frac{(\sqrt{3}-1)^2}{(\sqrt{3}+1)(\sqrt{3}-1)}=
(
3
+1)(
3
−1)
(
3
−1)
2
=\frac{(\sqrt{3})^2+(1)^2-2\sqrt{3}}{(\sqrt{3})^2-(1)^2}=
(
3
)
2
−(1)
2
(
3
)
2
+(1)
2
−2
3
=\frac{3+1-2\sqrt{3}}{3-1}=
3−1
3+1−2
3
=\frac{4}{2}-\frac{2\sqrt{3}}{2}=
2
4
−
2
2
3
=2-\sqrt{3}=2−
3
Now equating with RHS = a + b√3
we get a = 2 7 b = -1
Therefore, a = 2 and b = -1
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