Question

va rog cat mai repede

sa fiba rezolvate prin ecuații iraționale
3x+5=√3-x
x-√x=30
(x²-4)×√x+1=0
√2x-1=√x-1=√2x-3​

Answer 1

$a) \: 3x + 5 = \sqrt{3} - x \\ 3 x +x = \sqrt{3} - 5 \\ 4x = \sqrt{3} - 5 \\ x = \frac{ \sqrt{3} - 5 }{4} \\ \\ \\ b) \: x - \sqrt{x} = 30 \\ \sqrt{x} = x - 30 \\ x = (x - 30) {}^{2} \\ x = x {}^{2} - 60x + 900 \\ 61x - x {}^{2} - 900 = 0 \\ x {}^{2} - 61x + 900 = 0 \\ x {}^{2} - 25x - 36x + 900 = 0 \\ x(x - 25) - 36(x - 25) = 0 \\ (x - 36)(x - 25) = 0 \\ x - 36 = 0\implies \: x = 36 \\ x - 25 = 0\implies \: x = 25 \\ verificare : \\ 36 - \sqrt{36} = 5\implies \: \: adevarat \\ 25 - \sqrt{25} = 5\implies \: \: fals \\ \iff \: x = 36 \\ \\ \\ c) \: (x {}^{2} - 4) \sqrt{x + 1} = 0 \\ x {}^{2} - 4 = 0\implies x {}^{2} = 4\implies \: x = 2. \\ \implies x = - 2 \\ \sqrt{x + 1} = 0\implies \: x = - 1 \\ \iff \: x _{1} = 2 \\ \iff \: x _{2} = - 1$