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Prove that the value of each the followi...

Prove that the value of each the following determinants is zero: `|(a^x+a^(-x))^2(a^x-a^(-x))^2 1(b^y+b^(-y))^2(b^y-+b^(-y))^2 1(c^z+c^(-z))^2(c^z-c^(-z))^2 1|`

A

`a^(x)b^(y)c^(z)`

B

`a^(-x)b^(-y)c^(-z)`

C

`a^(2x)b^(2y)c^(2z)`

D

zero

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The correct Answer is:
D
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Prove that the value of each the following determinants is zero: (a^(x)+a^(-x))^(2),(a^(x)-a^(-x))^(2),1(b^(y)+b^(-y))^(2),(b^(y)-+b^(-y))^(2),1(c^(z)+c^(-z))^(2),(c^(z)-c^(-z))^(2),1]|

If a,b,c>0 and x,y,z in R then |[(a^x+a^(-x))^2, (a^x-a^(-x))^2, 1] , [(b^y+b^(-y))^2, (b^y-b^(-y))^2, 1], [(c^z+c^(-z))^2, (c^z-c^(-z))^2, 1]|=

Knowledge Check

  • If a, b,c gt 0& x,y,z in R" then the determinant"[{:(,(a^(2)+a^(-2))^(2),(a^(x)-a^(x))^(2),1),(,(b^(y)+b^(-y))^(2),(b^(y)-b^(y))^(2),1),(,(c^(x)+c^(-2))^(2),(c^(x)-c^(-z))^(2),1):}]=

    A
    `a^(x)b^(y)c^(z)`
    B
    `a^(-x)b^(-y)c^(-z)`
    C
    `a^(2x)b^(2y)c^(2z)`
    D
    zero

  • The following steps are involved in finding the value of (a^(x+y))^(x-y)(a^(y+z))^(y-z)(a^(z+x))^(z-x) . Arrange them in sequantial order. (A) a^((x+y)(x-y).a^(y+z)(y-z).a^((z+x)(z-x)) (B) a^0=1 (C) a^(x^2-y^2).a^(y^2-z^2).a^(z^2-x^2) (D) a^(x^2-y^2+y^2-z^2+z^2-x^2)

    A
    ADCB
    B
    ACBD
    C
    ACDB
    D
    ADBC

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