Question

Answer 1

a: =>21xz-49xt+15yz-35yt=21xz-49yz+15xt-35ty

=>-64xt=-64yz

=>x/y=z.t

c: M=5x^4+5x^2y^2+4x^2y^2+4y^4+5y^2

=(x^2+y^2)(5x^2+4y^2)+5y^2

=25x^2+20y^2+5y^2

=25(x^2+y^2)=125

Answer 2

1. 

$\frac{7x+5y}{3x-7y}=\frac{7z+5t}{3z-7t}$

$\Rightarrow (7x+5y)(3z-7t)=(7z+5t)(3x-7y)$

$\Rightarrow 21xz-49xt+15yz-35yt=21xz-49yz+15xt-35yt$

$\Rightarrow -49xt+15yz=-49yz+15xt$

$\Rightarrow 64xt=64yz$

$\Rightarrow xt=yz$

$\Rightarrow \frac{x}{y}=\frac{z}{t}$

Answer 3

2. Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{3x-2y}{4}=\frac{2z-4x}{3}=\frac{4y-3z}{2}$

$=\frac{4(3x-2y)}{16}=\frac{3(2z-4x)}{9}=\frac{2(4y-3z)}{4}$

$=\frac{4(3x-2y)+3(2z-4x)+2(4y-3z)}{16+9+4}$

$=\frac{12x-8y+6z-12x+8y-6z}{29}=0$

$\Rightarrow 3x-2y=2z-4x=4y-3z=0$

$\Rightarrow 3x=2y; 2z=4x$

$\Rightarrow \frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ 

Ta có đpcm.

Answer 4

3.

$M=5x^4+9x^2y^2+4y^4+5y^2$

$=4(x^4+2x^2y^2+y^4)+x^4+x^2y^2+5y^2$

$=4(x^2+y^2)^2+x^2(x^2+y^2)+5y^2$
$=4.5^2+5x^2+5y^2$

$=100+5(x^2+y^2)=100+5.5=125$