Question:
solve the equation-xpower 4+ xpower2+ 1
Answer:
Let x2 = a
So, x4 = a2
Now,
x4 + x2 + 1
= a2 + a + 1
= a2 + a + 1 + a - a
= a2 + 2a + 1 - a
= (a + 1)2 - a
= (a + 1)2 - (√a)2
= (a + 1 + √a)*(a + 1 - √a)
Now, put the value of a, we get
(x2 + 1 + √x2 )*(x2 + 1 - √x2 )
= (x2 + 1 + x)*(x2 + 1 - x)
= (x2 + x + 1)*(x2 - x + 1)
So, x4 + x2 + 1 = (x2 + x + 1)*(x2 - x + 1)
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