If A and B are the two real values of for which the system of equations is consistent, then is

Question

If A and B are the two real values of $k$ for which the system of equations $x + 2 y + z = 1, x + 3 y + 4 z = k, x + 5 y + 10 z = k^{2}$ is consistent,

then $A^{2} + B^{2}$ is _______

Smart Achievers · Accepted Answer

(5)

Here $x + 2 y + z = 1, x + 3 y + 4 z = k, x + 5 y + 10 z = k^{2}$ and $Δ_{1} = Δ_{2} = Δ_{3} = 0 \Rightarrow k = 1, 2$ then $A^{2} + B^{2} = 1 + 4 = 5$

Solution

Q.
If A and B are the two real values of $k$ for which the system of equations $x + 2 y + z = 1, x + 3 y + 4 z = k, x + 5 y + 10 z = k^{2}$ is consistent,

then $A^{2} + B^{2}$ is _______

Ans.
(5)

Here $Δ = 0$ and $Δ_{1} = Δ_{2} = Δ_{3} = 0 \Rightarrow k = 1, 2$ then $A^{2} + B^{2} = 1 + 4 = 5$

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Solution

Q. If A and B are the two real values of k for which the system of equations x+2y+z=1, x+3y+4z=k, x+5y+10z=k2 is consistent, then A2+B2 is _______

Ans. (5) Here Δ=0 and Δ1=Δ2=Δ3=0⇒k=1,2 then A2+B2=1+4=5

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Q.
If A and B are the two real values of $k$ for which the system of equations $x + 2 y + z = 1, x + 3 y + 4 z = k, x + 5 y + 10 z = k^{2}$ is consistent,

then $A^{2} + B^{2}$ is _______

Ans.
(5)

Here $Δ = 0$ and $Δ_{1} = Δ_{2} = Δ_{3} = 0 \Rightarrow k = 1, 2$ then $A^{2} + B^{2} = 1 + 4 = 5$