Question

if (x - 5)(y + 6 )(z - 8)= 1331 then find the minimum value of x+y+z​

Answer 1

Step-by-step explanation:

solve:.

$(x - 5)(y + 6)(z - 8) \\ x(y + 6) - 5(y + 6)(z - 8) \\( xy + 6x - 5y - 30)(z - 8) \\ z(xy + 6x- 5y - 30) - 8(xy + 6x - 5y - 30) \\xyz + 6xz - 5yz - 30z - 8xy - 48x + 40y +240 \\xyz - 8xy + 6xz - 48x - 5yz + 40y - 30z + 240 \\ i \: hope \: it \: will \: help \: you \: mark \: me$

Answer 2

The minimum value of x+y+z is 40.

Step-by-step explanation:

Since we have given that

$(x - 5)(y + 6 )(z - 8)= 1331\\\\(x-5)(y+6)(z-8)=11^3\\\\(x-5)(y+6)(z-8)=11\times 11\times 11$

So, now equating each term of left hand side with corresponding each term of right hand side.

$x-5=11\\\\x=11+5\\\\x=16$

similarly,

$y+6=11\\\\y=11-6\\\\y=5$

Similarly,

$z-8=11\\\\z=11+8\\\\z=19$

So, Minimum value of x+y+z would  be

$x+y+z=16+5+19=40$

Hence, the minimum value of x+y+z is 40.

# learn more:

Factorise 1331 x³ - 343 y³​

https://brainly.in/question/10713464