Advertisements
Advertisements
Question
If `2"x"-1/(2"x")=4`, find : `4"x"^2+1/(4"x"^2)`
Sum
Advertisements
Solution
`2"x"-1/"2x"=4`
`⇒(2"x"-1/"2x")^2=(4)^2`
`⇒(2"x")^2+(1/"2x")^2-2xx2"x"xx1/"2x"=16`
`⇒4"x"^2+1/"4x"^2-2=16`
`⇒4"x"^2+1/"4x"^2=16+2`
`⇒4"x"^2+1/"4x"^2=18`
shaalaa.com
Application of Formulae
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
If `"a" + 1/"a"=3`, find `"a"^2+1/"a"^2`
If `"a" - 1/"a"=4`, find : `"a"^2+1/"a"^2`
Find : a + b + c, if a2 + b2 + c2 = 83 and ab + bc + ca = 71.
If a – b = 3 and ab = 10, find : a3 – b3.
Find : `"a"^3+1/"a"^3`, if `"a" +1/"a"=5`.
If `3"x"+1/(3"x")=3`, find : `27"x"^3+1/(27"x"^3)`
If a + b + c = 11 and a2 + b2 + c2 = 81, find : ab + bc + ca.
If 3x – 4y = 5 and xy = 3, find : 27x3 – 64y3.
If 5x – 4y = 7 and xy = 8, find : 125x3 – 64y3.
The difference between the two numbers is 5 and their products are 14. Find the difference between their cubes.
