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Which quadratic equation is equivalent to (x2 - 1)2 - 11(x2 - 1) + 24 = 0?
Solution:
The question is based on the standard form of a quadratic equation.
Let's write the equation in it's standard form.
(x2 - 1)2 - 11(x2 - 1) + 24 = 0
Consider (x2 - 1) as u
u2 - 11u + 24 = 0
u2 - 8u - 3u + 24 = 0
u(u - 8) - 3( u - 8) = 0 → by splitting the middle term
(u - 8) ( u - 3) = 0
(x2 - 1 - 8 )( x2 - 1 - 3) = 0 ---------> by putting (x2 - 1) = u
(x2 - 9 )( x2 - 4) = 0
Hence, x2 – 9 = 0 or x2 – 4 = 0 -----> [ similar to the quadratic equation ax2 + bx + c = 0 ]
Thus, (x2 - 9) = 0 or (x2 - 4) = 0 are the standard form of (x2 - 1)2 - 11(x2 - 1) + 24 = 0.
Which quadratic equation is equivalent to (x2 - 1)2 - 11(x2 - 1) + 24 = 0?
Summary:
(x2 - 9) = 0 or (x2 - 4) = 0 are the standard equivalent form to (x2 - 1)2 - 11(x2 - 1) + 24 = 0.
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