MEDIUM
JEE Main
IMPORTANT
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If 2y+2z-xa=2z+2x-yb=2x+2y-zc, show that x2b+2c-a=y2c+2a-b=z2a+2b-c.

Important Questions on Ratio

EASY
JEE Main
IMPORTANT
If a2+b2+c2x2+y2+z2=(ax+by+cz)2, show that x:a=y:b=z:c.
EASY
JEE Main
IMPORTANT
If l(my+nz-lx)=m(nz+lx-my)=n(lx+my-nz), prove that y+z-xl=z+x-ym=x+y-zn.
EASY
JEE Main
IMPORTANT
Show that the elimination of ax+cy+bz=0, cx+by+az=0, bx+ay+cz=0 is a3+b3+c3-3abc=0.
EASY
JEE Main
IMPORTANT

Eliminate x, y, z from the equations ax+hy+gz=0; hx+by+fz=0, gx+fy+cz=0.

EASY
JEE Main
IMPORTANT
If x=cy+bz, y=az+cx, z=bx+ay, show that x21-a2=y21-b2=z21-c2.
EASY
JEE Main
IMPORTANT
Given that a(y+z)=x, b(z+x)=y, c(x+y)=z. Prove that bc+ca+ab+2abc=1.
EASY
JEE Main
IMPORTANT

Solve the following equations:

3x-4y+7z=0, 2x-y-2z=0, 3x3-y3+z3=18

EASY
JEE Main
IMPORTANT

Solve the following equations:

x+y=z, 3x-2y+17z=0, x3+3y3+2z3=167