[" 17."(x+y-8)/(2)=(x+2y-14)/(3)=(3x+y-12)/(11)],[" HINT "a=b=c rArr a=b" and "b=c]

If (x+y-8)/2 = (x+2y-14)/3 = (3x+y-12)/11 , then find the values of x and y, respectively.

If (x+y)/(3a-b) = (y+z)/(3b-c) = (z+x)/(3c-a) , then show that (x+y+z)/(a+b+c)= (ax + by+cz)/(a^(2)+b^(2)+c^(2))

If 4x+5y=83 and (3x)/(2y)=(21)/(22), then y-x=?( a) 3( b) 4 (c) 7 (d) 11

If (x_(1)-x_(2))^(2) + (y_(1)-y_(2))^(2)=a^(2) , (x_(2)-x_(3))^(2) + (y_(2) - y_(3))^(2)=b^(2) , (x_(3)-x_(1))^(2) + (y_(3) - y_(1))^(2) = c^(2) and k[|(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|]^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c) then the value of k a)1 b)2 c)4 d)none of these

If (x+y)^(3)+8(x-y)^(3)=(3x+Ay)(3x^(2)+Bxy+Cy^(2)) , then the value of A+B+C is:

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

if (x_(1),x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

if (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)