Question

Maths Please Solve ​

Answer 1

Answer:

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Explanation:

x + y + z = √3

x²+y²+z² + 2 (xy + yz + zx) = 3 ..............................................1

tan⁻¹x + tan⁻¹y = π/2 - tan⁻¹z

                      = cot⁻¹z

                     = tan⁻¹(1/z)

tan⁻¹(x+y / 1-xy) = tan⁻¹(1/z)

⇒ (x+y) / (1-xy) = 1/z

solving, xy + yz + zx = 1 ..............................................2

from 1 and 2,               x² + y² + z² = 1

square of a num is positive, hence such a condition is possible only when

x² = y² = z²                                     [ ∴3x² = 1; x = 1/$\sqrt{3}$]

x = y = z                            [∵ x + y + z =  1/√3+1/√3+1/√3 = √3 ]

hence proved