Срочно!!!' Решите неравенство !!!!!

Question

Срочно!!!' Решите неравенство !!!!!

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Answer 1

X-1≥0⇒x≥1
x+2≥0⇒x≥-2
x∈[1;∞)
3√(x-1)>1+√(x+2)
9(x-1)>1+2√(x+2)+x+2
9x-9-x-3>2√(x+2)
8x-12>2√(x+2)
4x-6>√(x+2)
16x²-48x+36>x+2
16x²-49x+34>0
D=2401-2176=225
x1=(49-15)/32=17/16
x2=(49+15)/32=2
x<1/16 U x>2
x∈[1;17/16) U (2;∞)