Let A - x - x -1-3 and B - x - x 2-2 ax - a 2-4 - 0 be two sets- If A - B - x -2- x - 1- then the smallest positive integral value of -a -is

Let f(x)=x^2 2ax + a^2 4 ∵ A ∩ B ={x: 2 lt; x ≤ 1} ⋯ (1) ∴ . vertex amp;≥ amp;1 f(1) amp;≥ amp;0 }∩ ⋯ (2) (1)⇒ a ≥ 1 (2) ⇒ a^2 2a 3 ...

106

You visited us 106 times! Enjoying our articles? Unlock Full Access!

Condition for Two Lines to be on the Same Plane

Let A = x :| ...

Question

Let A = {x : |x-1|< 3} and B = {x : $x^{2}$ – 2ax + $a^{2}$ – 4 $\geq$ 0} be two sets. If $A \cap B = {x : - 2 < x \leq 1}$ , then the smallest positive integral value of ‘a’ is ___

Open in App

Solution

Suggest Corrections

Similar questions

x^{2} + a x + 12 = 0, x^{2} + b x + 15 = 0

x^{2} + (a + b) x + 36 = 0

a - b

x > 0,

A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} x + \frac{1}{x} & 0 & 0 0 & x & 0 0 & 0 & 16 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦

B = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{5 x}{x^{2} + 1} & 0 & 0 0 & \frac{3}{x} & 0 0 & 0 & \frac{1}{4} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

X

Y

X = (A B)^{- 1} + (A B)^{- 2} + {A B}^{- 3} + \dots (A B)^{- n}

Y = lim n \to \infty X

t r (P)

P

t r (A Y)

x_{1}

x_{2}

2 x^{2} + 6 x + b = 0.

\frac{x_{1}}{x_{2}} + \frac{x_{2}}{x_{1}} = k

b < 0,

| k |

A

B

A = {(x, y) : | x - 3 | < 1

| y - 3 | < 1}

B = {(x, y) : 4 x^{2} + 9 y^{2} - 32 x - 54 y + 109 \leq 0}

x^{2} + a x + 12 = 0,

x^{2} + b x + 15 = 0

x^{2} + (a + b) x + 36 = 0

a - b

Join BYJU'S Learning Program