Question

Diketahui sistem persamaan :
1) y + 2/(x+z) = 4
2) 5y + (18/(2x+y+z) = 18
3)8/(x+z) - 6/(2x+y+z) = 3

Nilai dari
y + √(x² - 2xz + z²) = ....​

Answer 1

pake pemisalan aja..

misalkan

a = 1/(x+z)

b = 1/(2x+y+z)

jadi :

1) y + 2a = 4

2) 5y + 18b = 18

3) 8a - 6b = 3

eliminasi pers 1 and pers 2..

y + 2a = 4. --> 5y + 10a = 28

5y + 18b = 18--> 5y + 18b = 18

--------------------------------------------- -

10a - 18b = 2..(4)

eliminasi pers 3 and pers 4

10a - 18b = 2 --> 10a - 18b = 2

8a - 6b = 3 --> 24a - 18b = 9

------------------------------------------- -

-14a = -7

a = 1/2

y + 2a = 4

y + 1 = 4

y = 3

8a - 6b = 3

4 - 6b = 3

-6b = -1

b = 1/6

a = 1/(x+z)

1/2 = 1/(x+z)

x + z = 2...(*)

b = 1/(2x+ y + z)

1/6 = 1/(2x + 3 + z)

2x + 3 + z = 6

2x + z = 3...(**)

eliminasi

x + z = 2

2x + z = 3

----------------

-x = -1

x = 1

z = 2-1 = 1

berarti

y + √(x² - 2xz + z²) =

y + √(x-z)² =

y + (x-z) =

3 + (1-1) =

3 + 0 =

3