Home
Class 12
MATHS
The equation (6-x)^4+(8-x)^4=16 has...

The equation `(6-x)^4+(8-x)^4=16` has

Text Solution

Verified by Experts

After a change of variable,
`y=((6-x)+(8-x))/2`
`:.y=7-x` or `x=7-y`
Now put `x=7-y` in given equation, we get
`(y-1)^(4)+(y+1)^(4)=16`
`impliesy^(4)+6y^(2)-7=0`
`=(y^(2)+7)(y^(2)-1)=0`
`y^(2)+7!=0`
[`y` gives imaginary values]
`:.y^(2)-1=0`
Then `y_(1)=-1` and `y_(2)=1`
Thus `x_(1)=8` and `x_(2)=6` are the roots of the given equation.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find all roots of the equation x^(6)-x^(5)+x^(4)-x^(2)+x-1=0.

One root of the equation 6x - 8x^3=sqrt3 is .........

The sum of the solutions of the equations 9^(x) - 6.3^(x) +8 = 0 is

Number of integral value (s) of k for which the equation 4x^(2)-16x+k=0 has one root lie between 1 and 2 and other root lies between 2 and 3, is

Solve the equation 3^(x-4)+5^(x-4)=34

If tan^(-1)y=4tan^(-1)x, (|x| lt tan(pi) /8) , find y as an algebraic function of x , and , hence, prove that tan(pi/8) is a root of the equation x^4-6x^2+1=0

If a,b,c and d are the roots of the equation x^(4)+2x^(3)+4x^(2)+8x+16=0 the value of the determinant |{:(1+a,1,1,1),(1,1+b,1,1),(1,1,1+c,1),(1,1,1,1+d):}| is

If the equation x^(4)-4x^(3)+ax^(2)+bx+1=0 has four positive roots, fond the values of a and b.

Find the real value of m for which the substitution y=u^m will transform the differential equation 2x^4y(dy)/(dx)+y^4=4x^6 in to a homogeneous equation.