You visited us 1 times! Enjoying our articles? Unlock Full Access!

Range

Let a,b,c be ...

Question

Let a,b,c be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x = c y + b z, y = a z + c x$ and $z = b x + a y .$
Then $a^{2} + b^{2} + c^{2} + 2 a b c$ is equal to

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $1$
For $x, y, z$ not to be simultaneously zero determinant of the coefficients should be zero.

$∣ ∣ ∣ ∣ \begin{matrix} - 1 & c & b c & - 1 & a b & a & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$

$\Rightarrow a^{2} + b^{2} + c^{2} + 2 a b c = 1$

Suggest Corrections

Similar questions

Let a,b,c,be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x= cy +bz, y=az + cx and z = bx +ay. Then , a² + b²+ c²+ 2abc is equal to

Q. Let

a, b, c

be any real numbers. Suppose that there are real numbers

x, y, z

not all zero such that

x = c y + b z, y = a z + c x

and

z = b x + a y

. Then

a^{2} + b^{2} + c^{2} + 2 a b c

is equal to

Q. Given,

x = c y + b z, y = a z + c x, z = b x + a y

, where x, y, z are not all zero, and a, b, c are real numbers. The value of

a^{2} + b^{2} + c^{2} + 2 a b c

Q. If

x = c y + b z, y = a z + c x, z = b x + a y

where

x, y, z

are not all zero, then

a^{2} + b^{2} + c^{2} + 2 a b c = k

Q. If

x = c y + b z, y = a z + c x, z = b x + a y

, where

x, y, z

are not all zero, then the value of

a^{2} + b^{2} + c^{2} + 2 a b c

Join BYJU'S Learning Program

Explore more

Range

Standard XI Mathematics

Join BYJU'S Learning Program

Let a,b,c be any real numbers. Suppose that there are real numbers x,y,z not all zero such that x=cy+bz,y=az+cx and z=bx+ay. Then a2+b2+c2+2abc is equal to

The correct option is B 1For x,y,z not to be simultaneously zero determinant of the coefficients should be zero. ∣∣ ∣∣−1cbc−1aba−1∣∣ ∣∣=0 ⇒a2+b2+c2+2abc=1

Let a,b,c be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x = c y + b z, y = a z + c x$ and $z = b x + a y .$
Then $a^{2} + b^{2} + c^{2} + 2 a b c$ is equal to

The correct option is B $1$
For $x, y, z$ not to be simultaneously zero determinant of the coefficients should be zero.

$∣ ∣ ∣ ∣ \begin{matrix} - 1 & c & b c & - 1 & a b & a & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$

$\Rightarrow a^{2} + b^{2} + c^{2} + 2 a b c = 1$