Question

The number of real roots of the equation (x + 3)4 + (x + 5)4 = 16 is

Solution

Correct option is

2

Let y = x + 4 so that given equation is (y – 1)4 + (y + 1)4 = 16

or 2(y4 + 6y2 + 1) = 16   or   y4 + 6y2 – 7 = 0

or (y2 + 7) (y2 – 1) = 0  ∴  

or x + 4 = ± 1

or x = – 3, – 5 are the only two real roots.

SIMILAR QUESTIONS

Q1

Let α and β are the roots of equation x2 + x + 1 = 0. The equation whose roots are α19, β7 is

Q2

If x2 + x + 1 is a factor ax3 + bx2 + cx + d, then the real root of ax3 + bx2cx + d = 0 is

Q3

If one root of the equation (a2 – 5a + 3)x2 + (3a – 1)x + 2 = 0 be double the other, then the value of α is:

Q4

For the equation 3x2 + px + 3 = 0, p > 0, if one of the roots is square of the other, then p is equal to

Q5

If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are real and less than 3, then

Q6

If b > a, then the equation (x – a) (x – b) – 1 = 0, has

Q7

If α and β (α < β), are the roots of the equation x2 + bx + c = 0, where c < 0 < b, then

Q8

If 1 lies between the roots of the equation 3x2 – 3 sin α x – 2 cos2 α = 0 then α lies in the interval

Q9

Let α,β be the roots of the equation x2 – px + r = 0 and  2β be the roots of the equation x2 – qx + r = 0. Then the value of r is

Q10

All the values of m for which both the roots of the equation x2 – 2mx + m2– 1 = 0 are greater than – 2 but less than 4, lie in the interval