1.

IF x+1/x=4,find(i) x²+1/x²(ii) x-1/x(iii) x³-1/x³plz helpfirst one will be brainliest PLZ WRITE CORRECT ASWER

Answer»

GIVEN : x + 1/x = 4

To FIND : (I) x² + 1/x²

(ii) x - 1/x

(iii) x³ - 1/x³

solution : as it is given that, x + 1/x = 4

squaring both sides we get,

(x + 1/x)² = 4²

⇒x² + 1/x² + 2 × x × 1/x = 16

⇒x² + 1/x² + 2 = 16

⇒x² + 1/x² = 14 ......(1)

(ii) we know, (a - b)² = (a + b)² - 4ab

⇒(x - 1/x)² = (x + 1/x)² - 4 × x × 1/x

⇒(x - 1/x)² = (4)² - 4

⇒(x - 1/x)² = 16 - 4 = 12

⇒(x - 1/x) = 2√3 .........(2)

(iii) we know, a³ - b³ = (a - b)³ + 3ab(a - b)

so, x³ - 1/x³ = (x - 1/x)³ + 3 × x × 1/x (x - 1/x)

= (2√3)³ + 3(2√3)

= 24√3 + 6√3 = 30√3

so, (x³ - 1/x³) = 30√3 .............(3)


Discussion

No Comment Found

Related InterviewSolutions