\(a^2+10\left(b^2+c^2\right)=\frac{a^2}{2}+8b^2+\frac{a^2}{2}+8c^2+2b^2+2c^2\)

\(\ge2\sqrt{\frac{a^2}{2}.8b^2}+2\sqrt{\frac{a^2}{2}.8c^2}+2\sqrt{2b^2.2c^2}\)

\(=4ab+4ac+4bc=4\)

Dấu \(=\)khi \(\hept{\begin{cases}\frac{a^2}{2}=8b^2=8c^2\\b^2=c^2\end{cases}}\Leftrightarrow a=4b=4c\).

Giải gấp nhé mấy bạn

đây nhé

...

A= x³ -30x² -31x +1

=x(x² -30x-31) +1

=x(x² +x -31x-31) +1

=x((x²+x) - (31x+31)) +1

=x (x(x+1) - 31(x+1)) +1

=x(x+1)(x-31) +1

Thay x=31 vào biểu thức A rút gọn ta được:

A= 31.(31+1)(31-31) +1

=31.31.0 +1

=0+1

=1

Vậy A=1

\(\left(x-1\right)^3-4x\left(x+1\right)\left(x-1\right)-3\left(x-1\right)\left(x^2+x+1\right)\)

\(=\left(x-1\right)^3-4x\left(x^2-1\right)-3\left(x^3-1\right)\)

\(=x^3-3x^2+3x-1-4x^3+4x-3x^3+3\)

\(=-6x^3-3x^2+7x+2\)

Nếu đề là: x−23=45x−23=45

x=45+23x=45+23

x=1215+1015x=1215+1015

→x=2215→x=2215

Nếu đề là: x−23=45x−23=45

x−3=45.3=125x−3=45.3=125

x=125+3x=125+3

x=125+155x=125+155

→x=275

minh cung vay

a) \(3x^4y^2-6x^3y^3+x^2y^4=x^2y^2\left(3x^2-6xy+y^2\right)\)

b) \(x^2-13x+36=x^2-4x-9x+36=x\left(x-4\right)-9\left(x-4\right)=\left(x-9\right)\left(x-4\right)\)

d) \(4x^2+4x-3=4x^2-2x+6x-3=2x\left(2x-1\right)+3\left(2x-1\right)=\left(2x+3\right)\left(2x-1\right)\)

c) \(3x^2-15x=3x\left(x-5\right)\)

e) \(x^2-10x+21=x^2-3x-7x+21=x\left(x-3\right)-7\left(x-3\right)=\left(x-3\right)\left(x-7\right)\).

f) \(8x^2+30x+7=8x^2+2x+28x+7=2x\left(4x+1\right)+7\left(4x+1\right)=\left(2x+7\right)\left(4x+1\right)\)