Question

5- square root 6 / 5+ square root 6= a - b square root 3, find the value of a and b
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Answer 1

Step-by-step explanation:

Given Question:-

(5-√6)/(5+√6)=a-b√3 then find the value of a and b?

Correction :-

(5-√6)/(5+√6) = a-b√6

To find:-

Find the value of a and b?

Solution:-

Given that

(5-√6)/(5+√6)=a-b√6

LHS :

(5-√6)/(5+√6)

Denominator = 5+√6

We know that

Rationalising factor of a +√b is a-√b

Rationalising factor of 5+√6 is 5-√6

On Rationalising the denominator then

=> [(5-√6)/(5+√6)] × [ (5-√6)/(5-√6)]

=> [(5-√6)(5-√6)]/[(5+√6)(5-√6)]

=> [(5-√6)]^2 /[5^2-(√6)^2]

(Since , (a+b)(a-b)=a^2-b^2)

=> [(5-√6)^2] /(25-6)

=> [(5-√6)^2] / 19

=> [ (5)^2 - 2(5)(√6) + (√6)^2]/19

(Since (a-b)^2=a^2-2ab+b^2)

=> [25-10√6+6]/19

=> (31-10√6)/19 =a-b√6

=> (31/19) - (10/19)√6 = a - b√6

On comparing both sides then

a = 31/19 and b = 10/19

Answer:-

The value of a = 31/19

The value of b = 10/19

Used formulae:-

• Rationalising factor of a +√b is a-√b
• (a-b)^2=a^2-2ab+b^2
• (a+b)(a-b)=a^2-b^2