1
Question
Solve the following equations.
(i) x4 29x2 + 100 = 0
(i) x4 29x2 + 100 = 0
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Solution
Given: x4 – 29x2 + 100 = 0
Let x2 = m
Then, the equation can be written as:
m2 – 29m + 100 = 0
On splitting the middle term –29m as –25m – 4m, we get:
m2 – 25m – 4m + 100 = 0
=> m(m – 25) –4(m – 25) = 0
=> (m – 25)(m – 4) = 0
=> m – 25 = 0 or m – 4 = 0
=> m = 25 or m = 4
On substituting m = x2, we get:
=> x2 = 25 or x2 = 4
=> x = ±5 or x = ±2
Thus, the solutions of the given equation are ±5, ±2.
Let x2 = m
Then, the equation can be written as:
m2 – 29m + 100 = 0
On splitting the middle term –29m as –25m – 4m, we get:
m2 – 25m – 4m + 100 = 0
=> m(m – 25) –4(m – 25) = 0
=> (m – 25)(m – 4) = 0
=> m – 25 = 0 or m – 4 = 0
=> m = 25 or m = 4
On substituting m = x2, we get:
=> x2 = 25 or x2 = 4
=> x = ±5 or x = ±2
Thus, the solutions of the given equation are ±5, ±2.
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