Question:৮ সরল কর `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x`, `(x > 0, y > 0, z > 0)`
Answer সমাধান: `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x` `= (x^-1 y)^(1/2) (y^-1 z)^(1/2) (z^-1 x)^(1/2)` `= (x^-1 y . y^-1 z . z^-1 x)^(1/2)` `= (x^(- 1 + 1) . y^(1 - 1) . z^(1 - 1))^(1/2)` `= (x^0 . y^0 . z^0)^(1/2)` `= (1 xx 1 xx 1)^(1/2)` `= 1` Ans.বিকল্প সমাধান: `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x` `= sqrt(1/x).y sqrt(1/y).z sqrt(1/z).x` `= sqrt(y/x) . sqrt(z/y) . sqrt(x/z)` `= sqrt(y)/sqrt(x) . sqrt(z)/sqrt(y) . sqrt(x)/sqrt(z)` `= 1` Ans.
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৮ shorol kar `sqrt(x^-1)y . sqrt(y^-1)z . sqrt(z^-1)x`, `(x > 0, y > 0, z > 0)`