TS EAMCET · Maths · Quadratic Equation
If \(\frac{x^2+x+1}{x^2+2 x+1}=A+\frac{B}{x+1}+\frac{C}{(x+1)^2}\), then \(A-B\) is equal to
- A \(4 C\)
- B \(4 C+1\)
- C \(3 C\)
- D \(2 C\)
Answer & Solution
Correct Answer
(D) \(2 C\)
Step-by-step Solution
Detailed explanation
\[ \frac{x^2+x+1}{x^2+2 x+1}=1-\frac{x}{x^2+2 x+1} \] Now, \(\frac{x}{x^2+2 x+1}=\frac{A}{(x+1)}+\frac{B}{(x+1)^2}\) \[ \Rightarrow \quad x=A(x+1)+B \] On equating the coefficient of \(x\) and constant, we get…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The solution of \(\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0\) is :TS EAMCET 2006 Medium
- If \(A, B\) and \(C\) are mutually exclusive and exhaustive events of a random experiment such that \(P(B)=\frac{3}{2} P(A)\) and \(P(C)=\frac{1}{2} P(B)\), then \(P(A \cup C)\) equals toTS EAMCET 2014 Medium
- \(\int_0^2 x^{\frac{5}{2}} \sqrt{2-x} d x=\)TS EAMCET 2023 Medium
- If the sum of two roots of the equation \(x^3-7 p x^2+5 q x-6 r=0\) is zero, thenTS EAMCET 2022 Medium
- If the length of the chord \(2 x+3 y+\mathrm{k}=0\) of the circle \(x^2+y^2-2 x+4 y-11=0\) is \(2 \sqrt{3}\), then the sum of all possible values of \(k\) isTS EAMCET 2025 Medium
- If \(\mathrm{L}_1, \mathrm{~L}_2\) and \(\mathrm{L}_3\) are the chords of contact of the three points \((2,0),(1,-2)\) and \((4,4)\) respectively with respect to the circle \(x^2+y^2=3\), then \(\mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3\) areTS EAMCET 2022 Medium
More PYQs from TS EAMCET
- If \(a, b\) and \(c\) form a geometric progression with common ratio \(r\), then the sum of the ordinates of the points of intersection of the line \(a x+b y+c=0\) and the curve \(x+2 y^2=0\) isTS EAMCET 2012 Medium
- Two slabs \(A\) and \(B\) of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab \(A\) is twice that of \(B\). The coefficient of thermal conductivity of slab \(A\) is twice that of \(B\). The first surface of slab \(A\) is maintained at \(100^{\circ} \mathrm{C}\), while the second surface of slab \(B\) is maintained at \(25^{\circ} \mathrm{C}\). The temperature at the contact of their surfaces isTS EAMCET 2008 Hard
- A bullet fired into a target losses one-third of its velocity after travelling a distance meter into the target. If the bullet comes to rest by travelling a further distance , then the ratio isTS EAMCET 2022 Easy
- A rifle of \(20 \mathrm{~kg}\) mass can fire 4 bullets per second. The mass of each bullet is \(35 \times 10^{-3} \mathrm{~kg}\) and its final velocity is \(400 \mathrm{~ms}^{-1}\). Then what force must be applied on the rifle so that it does not move backwards while firing the bullets ?TS EAMCET 2007 Easy
- Two bodies are projected from the same point with the same initial velocity ' \(u\) ' making angles ' \(\theta\) ' and \(\left(90^{\circ}-\theta\right)\) with the horizontal in opposite directions. The horizontal distance between their positions when the bodies are at their maximum heights isTS EAMCET 2025 Medium
- Particles and their anti-particles haveTS EAMCET 2005 Medium