Given: y2 + 8y +16 = 0 On splitting the middle term 8y as 4y + 4y, we get: y2 + 4y + 4y + 16 = 0 = gt; y(y + 4) + 4(y + 4) = 0 = gt; (y + 4) (y + 4) = 0 = ...

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Standard X

Mathematics

Componendo and Dividendo

y2+8 y+16=0

Question

y² + 8y +16 = 0

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Solution

Given: y² + 8y +16 = 0
On splitting the middle term 8y as 4y + 4y, we get:
y² + 4y + 4y + 16 = 0
=> y(y + 4) + 4(y + 4) = 0
=> (y + 4) (y + 4) = 0
=> (y + 4)² = 0
=> y + 4 = 0 or y = –4
Therefore, the solution of the given equation is y = –4.

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y2 + 8y +16 = 0

Given: y2 + 8y +16 = 0 On splitting the middle term 8y as 4y + 4y, we get: y2 + 4y + 4y + 16 = 0 => y(y + 4) + 4(y + 4) = 0 => (y + 4) (y + 4) = 0 => (y + 4)2 = 0 => y + 4 = 0 or y = –4 Therefore, the solution of the given equation is y = –4.

y² + 8y +16 = 0

Given: y² + 8y +16 = 0
On splitting the middle term 8y as 4y + 4y, we get:
y² + 4y + 4y + 16 = 0
=> y(y + 4) + 4(y + 4) = 0
=> (y + 4) (y + 4) = 0
=> (y + 4)² = 0
=> y + 4 = 0 or y = –4
Therefore, the solution of the given equation is y = –4.