Question

Tính nhanh:

85.75=

72^2+144.28+28^2=

Tính GTNN:

A=x^2-2x+5B=x^2+x+1C=4x^2+5x-3Ai lm đc mik tik cho!!!!

Answer 1

72^2+144.28+28^2=(72+28)²=100²=10000

Học tốt!!!!!!!!!!

Answer 2

A=x^2-2x+5

= (x²-2x+1)+4

=(x-1)²+4\(\ge\)4

Dấu "=" xảy ra khi x=1

Vậy......................

Answer 3

B=x^2+x+1

\(=\left(x+\frac{1}{2}\right)^2+\frac{1}{2}\ge\frac{1}{2}\)

Dấu "=" xảy ra khi \(x=\frac{-1}{2}\)

Vậy................................................

Answer 4

Thanks bn

Answer 5

Mình làm phần còn lại ha

\(85.75=\left(80+5\right)\left(80-5\right)=80^2-5^2=6375\)

\(C=4x^2+5x-3=\left(4x^2+5x+\frac{25}{16}\right)-\frac{73}{16}=\left[\left(2x\right)^2+2.2x.\frac{5}{4}+\left(\frac{5}{4}\right)^2\right]-\frac{73}{16}\)

\(C=\left(2x+\frac{5}{4}\right)^2-\frac{73}{16}\ge\frac{-73}{16}\)

Vậy \(GTNN_C=\frac{-73}{16}\)tại \(x=\frac{-5}{8}\)

Answer 6

A = x² - 2x + 5

Ta có: A = x² - 2x + 5 = (x² - 2x + 1) + 4 = (x - 1)² + 4

Ta luôn có : (x - 1)² \(\ge\)0 \(\forall\)x

=> (x - 1)² + 4 \(\ge\) 4\(\forall\)x

hay A \(\ge\) 4 \(\forall\)x

Dấu "=" xảy ra <=> (x - 1)² = 0 <=> x - 1 = 0 <=> x = 1

Vậy A_min = 4 tại x = 1

*) B = x² + x + 1 

Ta có: B = x² + x + 1 = (x² + x + 1/4) + 3/4 = (x + 1/2)² + 3/4

Ta luôn có: (x + 1/2)² \(\ge\)0 \(\forall\)x

=> (x + 1/2)² + 3/4 \(\ge\) 3/4 \(\forall\)x

hay A \(\ge\)3/4 \(\forall\)x

Dấu "=" xảy ra <=> (x + 1/2)² = 0 <=> x + 1/2 = 0 <=> x = -1/2

Vậy B_min = 3/4 tại x = -1/2

Answer 7

\(85.75=\left(80+5\right)\left(80-5\right)=80^2-5^2=6400-25=6375\)

Answer 8

\(72^2+144.28+28^2=72^2+2.72.28+28^2=\left(72+28\right)^2=100^2=10000\)