Please solve this question
Answers
Answer:
(√3-1)×2={2√3-2) is the answer
Answer:
Rationalize the denominator of \frac{2}{\sqrt{3}-1}
3
−1
2
by multiplying numerator and denominator by \sqrt{3}+1
3
+1.
2\sqrt{3}-\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}2
3
−
(
3
−1)(
3
+1)
2(
3
+1)
Step 2
Consider \left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)(
3
−1)(
3
+1). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}(a−b)(a+b)=a
2
−b
2
.
2\sqrt{3}-\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^{2}-1^{2}}2
3
−
(
3
)
2
−1
2
2(
3
+1)
Step 3
Square \sqrt{3}
3
. Square 11.
2\sqrt{3}-\frac{2\left(\sqrt{3}+1\right)}{3-1}2
3
−
3−1
2(
3
+1)
Step 4
Subtract 11 from 33 to get 22.
2\sqrt{3}-\frac{2\left(\sqrt{3}+1\right)}{2}2
3
−
2
2(
3
+1)
Step 5
Cancel out 22 and 22.
2\sqrt{3}-\left(\sqrt{3}+1\right)2
3
−(
3
+1)
Step 6
To find the opposite of \sqrt{3}+1
3
+1, find the opposite of each term.
2\sqrt{3}-\sqrt{3}-12
3
−
3
−1
Step 7
Combine 2\sqrt{3}2
3
and -\sqrt{3}−
3
to get \sqrt{3}
3
.
\sqrt{3}-1
3
−1