Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5

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To determine whether x is less than 5, we can evaluate the statements (1) and (2) separately.

Statement (1) x^2 > 5:
This statement indicates that the square of x is greater than 5. If x^2 is greater than 5, it means that x can be either positive or negative. For example, if x is 3, then 3^2 = 9, which is greater than 5. However, if x is -3, then (-3)^2 = 9, which is also greater than 5. Therefore, statement (1) alone does not provide enough information to determine whether x is less than 5.

Statement (2) x^2 + x < 5:
This statement suggests that the sum of x squared and x is less than 5. By rearranging the terms, we have x^2 + x - 5 < 0. This inequality is not easily solvable without further calculations. However, we can determine whether x is less than 5 by analyzing the quadratic equation x^2 + x - 5 = 0. If the roots of this equation are both less than 5, then the statement holds true. Calculating the roots of the equation, we find that they are approximately -2.791 and 1.791. Both of these roots are less than 5. Therefore, we can conclude that x is less than 5 based on statement (2).

Though, I got it wrong first. Here is my explanation by plugging values.

(1) x^2 > 5
x can be +10 or -10 to satisfy. Insufficient
(2) x^2 + x < 5
x can only be within range x<2 and X >-3 (Assuming fraction values as well). Sufficient.
Ans B.

Is x<5 ?

(1) x^2 > 5
this implies that x < -5 or x > 5.
For x < -5 ------ x< 5 - Yes
For x > 5 --------x < 5 - No
Not sufficient

(2) x^2 + x < 5
=> x(x+1) < 5
By plugging in values for x, we find that, this inequality is true for values of x in the range -> -3<x<2
For this range of x, x is less than 5.
Hence st2 is Sufficient.
Answer B

Hey , I guess you went wring in 2nd option
\(x(x + 1) < 5\)

\(x < 5\) or

\(x < 4\)

You treated this like equalities when there is an inequality sign, this is incorrect , rather do x*(x+1)<5 and plug in