Question

Factorise using suitable identity : 4x^2 + y^2 + 25z^2 + 4xy - 10yz -20zx  and hence evaluate for x = 3 , y = 2 and z = -2​

Answer 1

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This can be written in the form of

(-√2x)^2 + (y)^2 + (2√2z)^2 + 2(-√2)(1)xy + 2(1)(2√2)yz + 2(2√2)(-√2)xz

This is in the form of a^2+b^2+c^2 +2ab + 2bc + 2ca which is equal to (a+b+c)^2

Here a= -√2x b=y c=2√2

So it is simplified as

Ans. (-√2x+y+2√2z)^2

Answer 2

This can be written in the form of

(-√2x)^2 + (y)^2 + (2√2z)^2 + 2(-√2)(1)xy + 2(1)(2√2)yz + 2(2√2)(-√2)xz

This is in the form of a^2+b^2+c^2 +2ab + 2bc + 2ca which is equal to (a+b+c)^2

Here a= -√2x b=y c=2√2

So it is simplified as

Ans. (-√2x+y+2√2z)^2