If -3-1-3-1-a-b-3- then the value of -a- and -b- is

The correct option is A a=2 , b= 1 Given √( 3 ) 1 /√( 3 ) +1 =a+b√( 3 ) LHS =( √( 3 ) 1 ) #160; ^ 2 / 3 1 (Multiplying by ( √( 3 ) 1 ...

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Standard IX

Mathematics

Operations on Rational and Irrational Numbers

If √3-1/√3+...

Question

If $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a + b \sqrt{3}$ , then the value of 'a' and 'b' is

a = 2

b = - 1

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a = 2

b = 1

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a = - 2

b = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a = - 2

b = - 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $a = 2$ , $b = - 1$
Given
$\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a + b \sqrt{3}$
LHS
$= \frac{{(\sqrt{3} - 1)}^{2}}{3 - 1} (M u l t i p l y i n g b y (\sqrt{3} - 1) w i t h n u m e r a t o r a n d d e n o m i n a t o r)$
$= \frac{3 + 1 - 2 \sqrt{3}}{2}$
$= \frac{4 - 2 \sqrt{3}}{2}$
$= 2 - \sqrt{3}$
$= 2 - \sqrt{3} = a + b \sqrt{3}$
$a = 2, b = - 1$

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If √3−1√3+1=a+b√3, then the value of 'a' and 'b' is

The correct option is A a=2, b=−1Given√3−1√3+1=a+b√3LHS=(√3−1)23−1(Multiplyingby(√3−1)withnumeratoranddenominator)=3+1−2√32 =4−2√32=2−√3 =2−√3=a+b√3a=2,b=−1

If $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a + b \sqrt{3}$ , then the value of 'a' and 'b' is