Ifx(y+z)=16, y(z + x) = 66, z(x + y) = 70 and x,y,z > 0, then (x + y + z) is less than
Answers
Given : x(y+z) = 16, y(z + x) = 66, z(x + y) = 70 and x,y,z > 0,
To Find : (x + y + z)
Solution:
x(y + z) = 16 => xy + xz = 16
y(z + x) = 66 => yz + xy = 66
z(x + y) = 70 => xz + yz = 70
Adding all
=> 2( xy + yz + xz) = 152
=> xy + yz + xz = 76
xy + yz + xz = 76
xy + xz = 16 => yz = 60
yz + xy = 66 => xz = 10
xz + yz = 70 => xy = 6
Multiplying all (xyz)² = 60 * 10 * 6
=> xyz = 60
xyz = 60
yz = 60 => x = 1
xz = 10 => y = 6
xy = 6 => z = 10
x = 1 , y = 6 , z = 10
=> x + y + z = 1 + 6 + 10 = 17
x + y + z = 17
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Given : x(y+z) = 16, y(z + x) = 66, z(x + y) = 70 and x,y,z > 0,
To Find : (x + y + z)
Solution:
x(y + z) = 16 => xy + xz = 16
y(z + x) = 66 => yz + xy = 66
z(x + y) = 70 => xz + yz = 70
Adding all
=> 2( xy + yz + xz) = 152
=> xy + yz + xz = 76
xy + yz + xz = 76
xy + xz = 16 => yz = 60
yz + xy = 66 => xz = 10
xz + yz = 70 => xy = 6
Multiplying all (xyz)² = 60 * 10 * 6
=> xyz = 60
xyz = 60
yz = 60 => x = 1
xz = 10 => y = 6
xy = 6 => z = 10
x = 1 , y = 6 , z = 10
=> x + y + z = 1 + 6 + 10 = 17
x + y + z = 17
Learn More
(a+b+c)^2-100
brainly.in/question/15889846
a+b+c=3 a^2+b^2+c^2=6 1/a+1/b+1/c=1 find values of a , b and c
brainly.in/question/8061154
Write 5 examples of the form (a + b + c)² and expand them using the ...
brainly.in/question/11762738