Question

can you please answer this ...​

Answer 1

Answer:

157

Step-by-step explanation:

Given---> m√m + n√n = 550

m√n + n√m = 549

To find---> 13 ( m + n ) / 7 = ?

Solution---> ATQ,

m√m + n√n = 550 ...............................(1)

m√n + n√m = 549 ...............................(2)

Let √m = x and √n = y

So, m = x² and n = y²

Now from equation ( 1 )

m√m + n√n = 550

=> x² ( x ) + y² ( y ) = 550

=> x³ + y³ = 550 ............................(3)

Now from equation ( 2 )

m√n + n√m = 549

=> x²( y ) + y² ( x ) = 549

=> xy ( x + y ) = 549...............................(4)

Now we know that,

( x + y )³ = x³ + y³ + 3xy ( x + y )

Putting values of (x³ + y³) and xy(x + y ) from equation (3) and (4) . we get

=> ( x + y )³ = 550 + 3 ( 549 )

= 550 + 1647

= 2197

=> ( x + y )³ = ( 13 )³

Taking cube root of both sides , we get

=> x + y = 13

Now from equation(4)

xy(x + y ) = 549

Putting x + y = 13 in it we get

xy ( 13 ) = 549

=> xy = 549 / 13

Now , we know that

( x + y )² = x² + y² + 2xy

=> ( 13 )² = x² + y² + 2 ( 549 / 13 )

=> 169 = x² + y² + ( 1098 / 13 )

=> x² + y² = 169 - ( 1098 / 13 )

Putting x = √m and y = √n , we get

=> ( √m )² + ( √n )² = (2197 - 1098) / 13

=> m + n = 1099 / 13

Now,

13(m + n ) / 7 = 13( 1099 / 13 ) / 7

13 is cancel out

= 1099 / 7

= 157

Answer 2

Given :-----

• m(√m) + n(√n) = 550
• m(√n) + n(√m) = 549

To find :------

• 13/7(m+n)

Formula used :-----

• (√a)² = a
• (x+y)³ = x³ + y³ + 3xy(x+y)
• (x+y)² = x² + y² + 2xy

See solution in image now ......

_______________________________________

$\large\bold\star\underline\mathcal{Extra\:Brainly\:Knowledge:-}$

[1] ( a + b )² = a² + 2ab + b²

[2] ( a – b )² = a² – 2ab + b²

[3] ( a + b )³ = a³ + 3a² b + 3ab² + b³

[4] ( a – b )³ = a ³ – 3a² b + 3ab² – b³

[5] ( a + b )( a ² - ab + b² ) = a³ + b³

[6] ( a – b )( a ² + ab + b² ) = a³ – b³

$\mathcal{BE\:\:BRAINLY}$