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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.
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ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
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  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

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  17. Find the discriminant of the quadratic equation 2x^2-4x+3=0, and hence...

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