Math, asked by harshshivaay, 1 month ago

Find the value of a in the following :
5+2√3 / 7+4√3 = a - 6√3​

Answers

Answered by ITZURADITYAKING
1

Answer:

=a+b3

Since rationalization of c+da+b=c+da+b×c−dc−d

Taking L.H.S.

By rationalization,

7+435+23 = 7+435+23× 7−437−43

Since,   {(a+b)(a−b)=a2−b2}

            = [(7)2−(43)2](5+23

Answered by tennetiraj86
2

Step-by-step explanation:

Given :-

(5+2√3)/(7+4√3) = a-6√3

To find :-

Find the value of a ?

Solution:-

Given that :

(5+2√3)/(7+4√3) = a-6√3

On taking LHS :

(5+2√3)/(7+4√3)

The denominator = 7+4√3

The Rationalising factor of 7+4√3 = 7-4√3

On Rationalising the denominator then

=> [(5+2√3)/(7+4√3)]×[(7-4√3)/(7-4√3)]

=> [(5+2√3)(7-4√3)]/[(7+4√3)(7-4√3)]

=> [(5+2√3)(7-4√3)]/[7²-(4√3)²]

Since (a+b)(a-b) = a²-b²

=> [(5+2√3)(7-4√3)]/(49-48)

=> [(5+2√3)(7-4√3)]/(1)

=> [(5+2√3)(7-4√3)]

=> (5×7)+(5×-4√3)+(2√3×7)-(2√3×4√3)

=> 35-20√3+14√3-24

=> (35-24)+(14√3-20√3)

=> 11-6√3

Now given equation will be

=> 11-6√3 = a-6√3

On Comparing both sides then

=> a = 11

Answer:-

The value of a for the given problem is 11

Used formulae

  • The Rationalising factor of a+√b is a-√b
  • (a+b)(a-b) = a²-b²

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