Question

2. If x2 + y2 + z2 = 29 and xy + yz + zx = 26,
then the value of x+y+z is :​

Answer 1

Answer:

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Question ⤵

➡. If x2 + y2 + z2 = 29 and xy + yz + zx = 26,

then the value of x+y+z is?

Answer⤵

Given:-

➡ x²+y²+z²=29

➡ xy+yz+zx=26

to ask:-

➡ value of x+y+z

Using identity:-

(a+b+c) ²=a²+b²+c²+ 2ab+2bc+2ca

Solution ⤵

➡ (x+y+z) ²= x²+y²+z²+2xy+2yz+2zx

(using identity (a+b+c) ²=a²+b²+c²+ 2ab+2bc+2ca)

➡ (x+y+z) ²= x²+y²+z²+2(xy+yz+zx)

( putting the value of x²+y²+z²=29 and xy+yz+zy=26)

➡ (x+y+z) ²= 29+2×26

➡ (x+y+z) ²= 29+52

➡ (x+y+z) ²= 81

➡ (x+y+z) = √81

➡ (x+y+z) = 9

Hence the value of x+ y +z =9.

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Answer 2

The value of x + y + z = ± 9

Given :

x² + y² + z² = 29 and xy + yz + zx = 26

To find :

The value of x + y + z

Formula :

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that ,

x² + y² + z² = 29

xy + yz + zx = 26

Step 2 of 2 :

Find the value of x + y + z

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

⇒ (x + y + z)² = 29 + (2 × 26)

⇒ (x + y + z)² = 29 + 52

⇒ (x + y + z)² = 81

⇒ x + y + z = ± 9

Hence the value of x + y + z = ± 9

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