Question

If a=√7-√5,b=√5-√3,c=√3-√7 then find the value of a+b+c-2abc​

Answer 1

Answer:

20√5 - 4√7 - 10√3

Step-by-step explanation:

$\red{\boxed{\rm Solution}}$

Given,

a = √7 - √5

b = √5 - √3

c = √3 - √7

To find,

a + b + c - 2abc

Solution,

(√7 - √5) + (√5 - √3) + (√3 - √7) - 2(√7 - √5)(√5 - √3)(√3 - √7)

√7 - √5 + √5 - √3 + √3 - √7 - (2√7 + 2√5)(√5 - √3)(√3 - √7)

- (2√7√5 - 2√7√3 + 2√5√5 - 2√5√3)(√3 - √7)

- (2√35 - 2√21 + 2√25 - 2√15)(√3 - √7)

- (2√35 - 2√21 + 2 x 5 - 2√15)(√3 - √7)

- (2√35 - 2√21 + 10 - 2√15)(√3 - √7)

- (2√35√3 - 2√21√3 + 10√3 - 2√15√3 - 2√35√7 - 2√21√7 + 10√7 - 2√15√7)

- (2√105 - 2√(7 x 3 x 3) + 10√3 - 2√(5 x 3 x 3) - 2√(7 x 5 x 7) + 10√7 - 2√105)

- (2√105 - 6√7 + 10√3 - 6√5 - 14√5 + 10√7 - 2√105)

- [√7(10 - 6) - √5(6 + 14) + 10√3]

- [4√7 - 20√5 + 10√3]

20√5 - 4√7 - 10√3

Therefore,

a + b + c - 2abc = 20√5 - 4√7 - 10√3

Concepts which we have used in solving this question,

• k√a + k'√a = √a(k + k')
• √n² = n
• √a√b = √(ab)
• √a/√b = √(a/b)
• √a + √b ≠ √(a + b)
• √a - √b ≠ √(a - b)