Math, asked by adarshgyan, 6 hours ago

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

Answered by amitnrw
2

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

Answered by juanRicardo2
1

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

Similar questions