Let y-x2-3 x-1-x2-x-1- x - R- thenA- y -1- 5-3-B- y -1-3- 5-3- y -1-3- 3-D- y -1-3-

The correct option is A y y =x^2 +3x+1/x^2+x+1 ⇒ y x^2 +yx +y =x^2 +3x+1 ⇒ x^2(y 1)+x(y 3)+(y 1)=0 given x is real, Δ≥ 0 ⇒ (y 3)^2 4(y 1)^2 ≥ 0 ⇒ (3y 5)(y+ ...

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Byju's Answer

Standard XI

Mathematics

Equations Which Can Be Solved by Substituting t = tan(X/2)

Let y=x2+3 x+...

Question

Let y = $\frac{x^{2} + 3 x + 1}{x^{2} + x + 1}$ ∀ x $\in$ R , then

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y [-1 , 3 ]

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Solution

The correct option is A
y

$y = \frac{x^{2} + 3 x + 1}{x^{2} + x + 1} \Rightarrow y x^{2} + y x + y = x^{2} + 3 x + 1 \Rightarrow x^{2} (y - 1) + x (y - 3) + (y - 1) = 0 g i v e n x i s r e a l, Δ \geq 0 \Rightarrow (y - 3)^{2} - 4 (y - 1)^{2} \geq 0 \Rightarrow (3 y - 5) (y + 1) \leq 0 \Rightarrow y ϵ [- 1, \frac{5}{3}]$

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Let y = x2+3x+1x2+x+1 ∀ x ∈ R , then

The correct option is A y y=x2+3x+1x2+x+1⇒yx2+yx+y=x2+3x+1⇒x2(y−1)+x(y−3)+(y−1)=0givenxisreal,Δ≥0⇒(y−3)2−4(y−1)2≥0⇒(3y−5)(y+1)≤0⇒yϵ[−1,53]

Let y = $\frac{x^{2} + 3 x + 1}{x^{2} + x + 1}$ ∀ x $\in$ R , then