Question
If $$x = a + \frac{1}{a}$$ and $$y = a - \frac{1}{a},$$ then the value of x4 + y4 - 2x2y2 is?
Answer: Option C
$$\eqalign{
& x = a + \frac{1}{a} \cr
& {x^2} = {a^2} + \frac{1}{{{a^2}}} + 2 \cr
& {y^2} = {a^2} + \frac{1}{{{a^2}}} - 2 \cr
& {\text{Now, }} \cr
& {x^4} + {y^4} - 2{x^2}{y^2} \cr
& = {\left( {{x^2} - {y^2}} \right)^2} \cr
& = {\left( {{a^2} + \frac{1}{{{a^2}}} + 2 - {a^2} - \frac{1}{{{a^2}}} + 2} \right)^2} \cr
& = {\left( 4 \right)^2} \cr
& = 16 \cr} $$
Was this answer helpful ?
$$\eqalign{
& x = a + \frac{1}{a} \cr
& {x^2} = {a^2} + \frac{1}{{{a^2}}} + 2 \cr
& {y^2} = {a^2} + \frac{1}{{{a^2}}} - 2 \cr
& {\text{Now, }} \cr
& {x^4} + {y^4} - 2{x^2}{y^2} \cr
& = {\left( {{x^2} - {y^2}} \right)^2} \cr
& = {\left( {{a^2} + \frac{1}{{{a^2}}} + 2 - {a^2} - \frac{1}{{{a^2}}} + 2} \right)^2} \cr
& = {\left( 4 \right)^2} \cr
& = 16 \cr} $$
Was this answer helpful ?
More Questions on This Topic :
Question 1. If **Hidden Equation** = ?
Question 2. If **Hidden Equation** equal to?....
Question 3. If **Hidden Equation** = ?....
Question 5. If **Hidden Equation** is?....
Question 6. If **Hidden Equation** = ?
Question 9. If **Hidden Equation** is?
Question 10. If **Hidden Equation** is?
Latest Videos
Latest Test Papers
Submit Solution