Question

PLZ SOLVE THESE TWO QUESTION ... HURRY PLZ!!!

Answer 1

ask if any doubt comes

Answer 2

Final Answer : 4: (A) 36,81
5: (A) 1
Steps : 14
1)
$\frac{6 {x}^{2} - 5x - 3 }{ {x}^{2} - 2x + 6 } \leqslant 4 \\ = > 2 {x}^{2} + 3x - 27 \leqslant 0 \\ = > 2 {x}^{2} + 9x - 6x - 27 \leqslant 0 \\ = > 2x(x - 3) + 9(x - 3) \leqslant 0 \\ = > (x -3 )(2x + 9) \leqslant 0$
Implies. =>
$= > \frac{ - 2}{9} \leqslant x \leqslant 3$
Now,
Maximum value of
$4 {x}^{2} = 4 {( \frac{ - 9}{2} )}^{2} = 81$
Minimum value of 4x^2 is 4 * 3^2 = 36 .

Steps :15
1) Since, α is positive by given equation.
As 4α /(1+α^2) > = 1 ,
Since, 1 + α^2 is positive
=> 4α is always positive.


After seeing pic calculation we get,
2<= α + 1/α <= 4

Here, α + 1/ α is 3 only is odd positive integer.

So, No. of Solution is 1 .