13.Simplify by rationalising the denominator:(5/7-√2)+(4/7+√2)​

2 thoughts on “13.Simplify by rationalising the denominator:(5/7-√2)+(4/7+√2)​”

1. Answer:

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   Step-by-step explanation:

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2. What is the value of “a” and “b” if (5+2√3)/(7+4√3)=a+b√3?

   Sachidanand Das

   Answered 2 years ago

   Answer: a=11, b=-6

   Solution:

   Given (5 + 2√3)/(7 + 4√3) = a + b√3

   Rationalizing the denominator on left-hand-side by multiplying the numerator and denominator with (7 – 4√3),

   (5 + 2√3) (7 – 4√3)/(7 + 4√3) (7 – 4√3) = a + b√3

   Multiply term by term the two expressions on numerator of L.H.S. and for the denominator apply the identity (m+n) (m-n) = m² – n² . We obtain,

   (35 – 20√3 + 14√3 – 8.√3.√3)/[7² – (4√3)²] = a + b√3

   Or, (35 – 6√3 – 8.3)/(49 – 48) = a + b√3

   Or, (35 – 6√3 – 24)/1 = a + b√3

   Or, 11 – 6√3 = a + b√3

   Now equate the rational and irrational terms from both sides.

   11 = a

   Or, a = 11

   – 6√3 = b√3

   ⇒ b = -6

   Verification:

   To prove (5 + 2√3)/(7 + 4√3) = a + b√3

   i.e. to prove (5 + 2√3) = (a + b√3) (7 + 4√3)

   Substituting for a=11 and b=-6,

   R.H.S.= (a + b√3) (7 + 4√3)

   = (11 – 6√3) (7 + 4√3) = 11.7 + 11.4√3 – 6√3.7 – 6.4.√3.√3 = 77 + 44√3 – 42√3 – 24.3

   = 77 + 2√3 – 72 = 5 + 2√3 = L.H.S.

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