If 4/1+√(2)+√(3) = a + b√(2) + c√(3) – d√(6), where a, b, c, d are nature numbers, then the value of a + b + c + d is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 4.
| Understanding | Application |
| Multiply numerator and Denominator by of L.H.S by 1+√(2)-√(3) |
{4/1+√(2)+√(3)} x (1+√(2)-√(3))/(1+√(2)-√3) = a + b√(2) + c√(3) – d√(6) {4 x (1+√2-√3)}/{(3 + 2√2) - (√3)2} =a + b√(2) + c√(3) – d√(6) {4 x (1+√2-√3)} / 2√2 = a + b√(2) + c√(3) – d√(6) 2 + √2 - √6 = a + b√(2) + c√(3) – d√(6) By comparing both sides. a = 2, b = 1, c = 0 and d = 1 Now, a + b + c + d = 2 + 1 + 0 + 1 = 4 So the value of a + b + c + d = 4 |