Let a-b-c are positive real number then the system of equations x2a2 - y2b2 - z2c2 - 1- x2a2 - y2b2 - z2c2 - 1- - x2a2 - y2b2 - z2c2 - 1 has

The correct option is B Unique solution x^2a^2+y^2b^2 z^2c^2=1 ........... (1) x^2a^2 y^2b^2+z^2c^2=1 ............ (2) x^2a^2+y^2b^2 ...

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Standard XII

Mathematics

Consistency of Linear System of Equations

Let a,b,c a...

Question

Let $a, b, c$ are positive real number then the system of equations
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1, \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1, \frac{- x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1$ has

No solution

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Unique solution

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Infinitely many solution

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Finite solution

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Solution

The correct option is B Unique solution
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1$ ........... $(1)$ $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1$ ............ $(2)$
$\frac{- x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1$ .......... $(3)$
Put $(\frac{x^{2}}{a}) = l {(\frac{y}{b})}^{2} = m {(\frac{z}{c})}^{2} = n$
$l t m - n = 1$ ...... $(4)$
$l - m + + n = 1$ ........ $(5)$
$- l + m + n = 1$ ........ $(6)$
On solving
$l = 1, m = 1, n = 1$
$x = a, y = b, z = c$
Unique solution
$B$ is correct

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Let a,b,c are positive real number then the system of equations x2a2+y2b2−z2c2=1,x2a2−y2b2+z2c2=1,−x2a2+y2b2+z2c2=1 has

The correct option is B Unique solutionx2a2+y2b2−z2c2=1 ........... (1) x2a2−y2b2+z2c2=1 ............ (2)−x2a2+y2b2+z2c2=1 .......... (3)Put (x2a)=l(yb)2=m(zc)2=nltm−n=1 ...... (4)l−m++n=1 ........ (5)−l+m+n=1 ........ (6)On solving l=1,m=1,n=1x=a,y=b,z=cUnique solution B is correct

Let $a, b, c$ are positive real number then the system of equations
$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1, \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1, \frac{- x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1$ has