Question

x,y,z apartin Q d. p. (3,4,5)
a)x+y+z=84
b)x+2y+3z=52
c)3x+4y+5z=50
d)2+2+2=200
x y z
e)1/x+1/y+1/z=42/80

Answer 1

x/3=y/4=z/5      y=4x/3    z=5x/3
a)x+y+z=84
x+4x/3+5x/3=84
3x+4x+5x=252
12x=252
x=21
y=4*21/3=28
z=5*21/3=35

b)x+2y+3z=52
x+2*4x/3+3*5x/3=52
3x+8x+15x=156
26x=156
x=6
y=4*6/3=8
z=5*6/3=10

c)3x+4y+5z=50
3x+4*4x/3+5*5x/3=50
9x+16x+25x=150
50x=150
x=3
y=4*3/3=4
z=5*3/3=5

d) x²+y²+z²=200
x²+(4x/3)²+(5x/3)²=200
x²+16x²/9+25x²/9=200
9x²+16x²+25x²=1800
50x²=1800
x²=36
x=6
y=4*6/3=8
z=5*6/3=10

e)1/x+1/y+1/z=42/80
1/x+1/(4x/3)+1/(5x/3)=21/40
1/x+3/4x+3/5x=21/40
(20+15+12)/20x=21/40
47/20x=21/40
x=47*40/20*21=94/21
y=4/3 * 94/21 =376/63
z=5/3 *94/21=470/63