x-y-z-4-z-t-x-3-y-z-t-4-t-x-y-1-find-the-value-of-x-2-y-2-z-2-t-2-

Question Number 90225 by jagoll last updated on 22/Apr/20

x + y + z = 4

z + t + x = - 3

y + z + t = 4

t + x + y = 1

find the value of x^{2} + y^{2} + z^{2} + t^{2}

Commented by niroj last updated on 22/Apr/20

x + y + z =

x + y = 4 - z \dots . . (i)

t + x + y = 1 \dots (iv)

from (i) & (iv)

t + 4 - z = 1

t - z = - 3 \dots . (v)

(ii) + (iii)

z + t + x = - 3

\frac{y + z + t = 4}{2 t + 2 z + x + y = 1}

2 t + 2 z + 4 - z = 1 (∵ x + y = 4 - z)

2 t + z = - 3 \dots (vi)

(v) + (vi)

t - z = - 3

\frac{2 t + z = - 3}{3 t = - 6}

t = - 2

t^{2} = 4

put the value of t in (v)

t - z = - 3

t + 3 = z

z = 3 - 2 = 1

z^{2} = 1

put the value of t, z in (ii)

z + t + x = - 3

1 - 2 + x = - 3

x = - 3 + 1

x = - 2

x^{2} = 4

put the value of x & z in (i)

x + y + z = 4

- 2 + y + 1 = 4

y = 4 + 1 = 5

y^{2} = 25

∴ x^{2} + y^{2} + z^{2} + t^{2} = 4 + 25 + 1 + 4 = 34 .

Commented by Prithwish Sen 1 last updated on 22/Apr/20

adding all 4 equations

x + y + z + t = 2 \dots \dots (v)

now

(v) - (i) t = 2

(v) - (ii) y = 5

(v) - (iii) x = - 2

(v) - (iv) z = 1

∴ x^{2} + y^{2} + z^{2} + t^{2} = 4 + 25 + 1 + 4 = 34

Commented by jagoll last updated on 22/Apr/20

thank you all

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