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1. True : x is a positive fraction 2. True : x^2(x^3 + x^2) < x^3 + x^2 3. True : -x^2(x^3 -x^2) < x^3 - x^2 : -x^2 < 1 (x is positive)Can you confirm the answer?

you cannot solve the inequality as it is. you are solving the inequality as if the given inequality is correct. also when you divide the inequality by -ves, the inequality should be fliped.

lets not go after who said what and what is OA given?

do you agree that (X^4 - X^5) is +ve and (X^3 - X^2) is -ve since x is a fraction. you tell me, which is greater? i am 100% sure that statememnt 3 is not correct as given by you.

Can some one help me with the working for option 3?

2 times I checked the attached Q Statement 3 should be

X^4 - X^5 < x^2 - x^3 In that case x^4(1-x) < x^2(1-x) x^4-x^2<0 x^2( x^2-1) < 0 x^2 cannot be -ve Hence x^2-1 < 0 which implies 0<x<1 Hence True Hence (3) is true. (1) & (2) are true as shown be4

Heman

Heman, I guess you went wrong in one place.
when x^4(1-x) < x^2(1-x)
You divided by (1-x) on both sides, to get x^4-x^2<0.
But you cant do this in inequalities, since you dont know what the value of 1-x is. If the value is negative the inequality sign needs to be reversed.
Hence (3) is false.

Can some one help me with the working for option 3?

2 times I checked the attached Q Statement 3 should be

X^4 - X^5 < x^2 - x^3 In that case x^4(1-x) < x^2(1-x) x^4-x^2<0 x^2( x^2-1) < 0 x^2 cannot be -ve Hence x^2-1 < 0 which implies 0<x<1 Hence True Hence (3) is true. (1) & (2) are true as shown be4

Heman

Heman, I guess you went wrong in one place. when x^4(1-x) < x^2(1-x) You divided by (1-x) on both sides, to get x^4-x^2<0. But you cant do this in inequalities, since you dont know what the value of 1-x is. If the value is negative the inequality sign needs to be reversed. Hence (3) is false.

yessuresh

U can divide in this case since Qstem states that x is +ve 0<x<1