Question

[Quyen Nguyen]

1) Tính nhanh:

52²+48²+96.52

2) Rút gọn :

(1-2x)(5x-7)

3) CM:

x - x^2 - 1 < 0 với mọi số thực x.

Giup mjk vs mjk đag cần gâp.

Answer 1

[Y]

1) \(52^2+48^2+52\cdot96\)

\(=52^2+2\cdot52\cdot48+48^2\)

\(=\left(52+48\right)^2=100^2=10000\)

2) \(\left(1-2x\right)\left(5x-7\right)=\left(5x-7\right)-2x\left(5x-7\right)\)

\(=5x-7-10x^2+14x\)

\(=-10x^2+19x-7\)

3) \(x-x^2-1=-\left(x^2-x+1\right)\)

\(=-\left(x^2-2x\cdot\frac{1}{2}+\frac{1}{4}+\frac{3}{4}\right)\)

\(=-\left(x-\frac{1}{2}\right)^2-\frac{3}{4}< 0\forall x\)