if t^2-2t+1=0, then the value of (t^6+1/t^6) is.
Answers
Answer :
t^6 + 1/t^6 = 2
Solution :
- Given : t² - 2t + 1 = 0
- To find : t^6 + 1/t^6 = ?
We have ;
=> t² - 2t + 1 = 0
=> t² + 1 = 2t
=> (t² + 1)/t = 2
=> t²/t + 1/t = 2
=> t + 1/t = 2
Now ,
Squaring both sides , we get ;
=> (t + 1/t)² = 2²
=> t² + 2•t•(1/t) + (1/t)² = 4
=> t² + 2 + 1/t² = 4
=> t² + 1/t² = 4 - 2
=> t² + 1/t² = 2
Now ,
Cubing both sides , we get ;
=> (t² + 1/t²)³ = 2³
=> (t²)³ + (1/t²)³ + 3•t•(1/t)•(t + 1/t) = 8
=> t^6 + 1/t^6 + 3•2 = 8
=> t^6 + 1/t^6 + 6 = 8
=> t^6 + 1/t^6 = 8 - 6
=> t^6 + 1/t^6 = 2
Hence ,
t^6 + 1/t^6 = 2
×××××××××××××××××××××××××××××××
Note :
If x + 1/x = 2 , then x = 1 and 1/x = 1
Thus ,
x² + 1/x² = 2
x³ + 1/x³ = 2
x⁴ + 1/x⁴ = 2
.
.
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xⁿ + 1/xⁿ = 2
Answer:
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Step-by-step explanation:
Hydrogen peroxide is a chemical compound with the formula H ₂O ₂. In its pure form, it is a very pale blue liquid, slightly more viscous than water. Hydrogen peroxide is the simplest peroxide. It is used as an oxidizer, bleaching agent, and antiseptic.
→Formula: H2O2
→IUPAC ID: hydrogen peroxide
→Molar mass: 34.0147 g/mol
→Density: 1.45 g/cm³
→Boiling point: 150.2 °C
→Melting point: -0.43 °C
What is hydrogen peroxide common name?
\huge\mathrm{\pink{Answer}}Answer
Hydrogen peroxide, dihydrogen dioxide, hydrogen dioxide, hydrogen oxide, oxydol, peroxide.
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HOPEIT HELPS
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