Question

a ) Cho x - y + z = 0 . Chứng minh : xy + yz - zx > 0

b ) 8 . 2ⁿ + 2ⁿ⁺¹ \(⋮\) 10

Answer 1

a) x - y + z = 0

<=> (x - y + z)² = 0

<=> (x - y + z).x - (x - y + z).y + (x - y + z).z = 0

<=> x² - xy + xz - xy + y² - zy + xz - zy + z² = 0

=> x² + y² + z² - 2xy + 2xz - 2zy = 0

=> x² + y² + z² = 2xy - 2xz + 2zy = 2.(xy - xz + yz)

Vì \(x^2+y^2+z^2\ge0\) nên \(2.\left(xy-xz+yz\right)\ge0\)

\(\Leftrightarrow xy-xz+yz\ge0\left(đpcm\right)\)

b) ĐK: x ϵ N

\(8.2^n+2^{n+1}=8.2^n+2^n.2=2^n.\left(8+2\right)=2^n.10⋮10\)

Answer 2

a mik ko biết

b. 8.2^n +2^(n+1)

A= 8. 2^n + 2^n +2

=2^n(8+2)

=2^n.10

vậy A chia hết cho 10 (đpcm)

Answer 3

tik mik vs