Question

factorise this sum
${x}^{2} - 6 \sqrt{2x} + 18$

Answer 1

Hello !!




X² - 6✓2 X + 18





Coefficient of X² = 1 and Constant term = 18.



Product of 1 and 18 = 18.


We try to split 18 in two parts such that their sum of subtraction should be equal to 6✓2 and product should be 18.



Clearly,




-3✓2 - 3✓2 = -6✓2



and,


-3✓2 × -3✓2 = 18



So,



X² - 6✓2 X + 18



X² - 3✓2 X - 3✓2 X + 18




X ( X - 3✓2 ) - 3✓2 ( X - 3✓2 )




( X - 3✓2 ) ( X - 3✓2 ) = 0




X = 3✓2 or X = 3✓2.





Hence,


The given quadratic polynomial have two equal zeroes which are 3✓2 and 3✓2.



Hope it will help you :-)

Answer 2

Here is your answer

x²-6root2 + 18
x²-3root2x-3root2x+18
x(x-3root2)-3root(x-3root2)
(x-3root2)(x-3root2)

x = 3root2.

Hope it helps you^_^