Question

X + Y + Z is equal to 10, X square + Y square + Y square equal to 60 find X Y + Y Z + ZX

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given:

$\rm:\longmapsto x + y + z = 10 - (i)$

$\rm:\longmapsto {x}^{2} + {y}^{2} + {z}^{2} =60$

Squaring both sides of (i), we get:

$\rm:\longmapsto (x + y + z)^{2} = 10 0$

$\rm:\longmapsto {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + xz) = 100$

Substitute the value of x² + y² + z², we get:

$\rm:\longmapsto 60 + 2(xy + yz + xz) = 100$

$\rm:\longmapsto 2(xy + yz + xz) = 100 - 60$

$\rm:\longmapsto xy + yz + xz= \dfrac{40}{2}$

$\rm:\longmapsto xy + yz + xz= 20$

★ So, the value of xy + yz + xz is 20.

$\textsf{\large{\underline{Answer}:}}$

• The value of xy + yz + xz is 20.

$\textsf{\large{\underline{More Identities To Know}:}}$

1. (a + b)² = a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
3. a² - b² = (a + b)(a - b)
4. (a + b)³ = a³ + 3ab(a + b) + b³
5. (a - b)³ = a³ - 3ab(a - b) - b³
6. a³ + b³ = (a + b)(a² - ab + b²)
7. a³ - b³ = (a - b)(a² + ab + b²)
8. (a + b + c)² = a² + b² + c² + 2(ab + bc + ac)

Answer 2

Answer:

HEY BUDDY,

Step-by-step explanation:

$[tex]\textsf{\large{\underline{Solution}:}}$

Given:

$\rm:\longmapsto x + y + z = 10 - (i)$

$\rm:\longmapsto {x}^{2} + {y}^{2} + {z}^{2} =60$

Squaring both sides of (i), we get:

$\rm:\longmapsto (x + y + z)^{2} = 10 0$

$\rm:\longmapsto {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + xz) = 100$

Substitute the value of x² + y² + z², we get:

$\rm:\longmapsto 60 + 2(xy + yz + xz) = 100$

$\rm:\longmapsto 2(xy + yz + xz) = 100 - 60$

$\rm:\longmapsto xy + yz + xz= \dfrac{40}{2}$

$\rm:\longmapsto xy + yz + xz= 20$

★ So, the value of xy + yz + xz is 20.

$\textsf{\large{\underline{Answer}:}}$

The value of xy + yz + xz is 20.

$\textsf{\large{\underline{More Identities To Know}:}}$

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)[/tex]