√(4x + 91) - √(11x + 1) - √(7x + 4) = 0
одз 4x + 91 >=0 x>=-91/4
11x + 1>=0 x>=-1/11
7x+4>=0 x>=-4/7
x >=-1/11
√(4x + 91) - √(7x + 4) = √(11x + 1) возводим в квадрат
4x + 91 - 2√(4x + 91)√(7x + 4) + 7x + 4 = 11x + 1
11x + 95 - 2√(4x + 91)√(7x + 4) - 11x - 1 = 0
√(4x + 91)√(7x + 4) = 47
(4x + 91)(7x + 4) = 47²
28x² + 16x + 637x + 364 - 2209 = 0
28x² + 653x - 1845 = 0
D = 426409 + 206640 = 633049 (≈796²)
x₁₂ = (-653 +- √633049)/56
x1 = (-653 - √633049)/56 < -1/11 не корень
x2=(-653 + √633049)/56
√(4x + 91) - √(11x + 1) - √(7x + 4) = 0
одз 4x + 91 >=0 x>=-91/4
11x + 1>=0 x>=-1/11
7x+4>=0 x>=-4/7
x >=-1/11
√(4x + 91) - √(7x + 4) = √(11x + 1) возводим в квадрат
4x + 91 - 2√(4x + 91)√(7x + 4) + 7x + 4 = 11x + 1
11x + 95 - 2√(4x + 91)√(7x + 4) - 11x - 1 = 0
√(4x + 91)√(7x + 4) = 47
(4x + 91)(7x + 4) = 47²
28x² + 16x + 637x + 364 - 2209 = 0
28x² + 653x - 1845 = 0
D = 426409 + 206640 = 633049 (≈796²)
x₁₂ = (-653 +- √633049)/56
x1 = (-653 - √633049)/56 < -1/11 не корень
x2=(-653 + √633049)/56