Question:
If $(x+1 / x)=5$, Find the value of $x^{3}+1 / x^{3}$
Solution:
Given, $(x+1 / x)=5$
We know that, $(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b)$ ... 1
Substitute (x + 1/x) = 5 in eq1
$(x+1 / x)^{3}=x^{3}+1 / x^{3}+3\left(x^{*} 1 / x\right)(x+1 / x)$
$5^{3}=x^{3}+1 / x^{3}+3(x * 1 / x)(x+1 / x)$
$125=x^{3}+1 / x^{3}+3(x+1 / x)$
$125=x^{3}+1 / x^{3}+3(5)$
$125=x^{3}+1 / x^{3}+15$
$125-15=x^{3}+1 / x^{3}$
$x^{3}+1 / x^{3}=110$
Hence, the result is $x^{3}+1 / x^{3}=110$
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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