Explanation:
2).
Given that 1/(7+5√2)
We know that
The Rationalising factor of a+√b is a-√b
The denominator = 7+5√2
The Rationalising factor of 7+5√2 is 7-5√2
On Rationalising the denominator then
=> [1/(7+5√2)]×[ (7-5√2)/(7-5√2)]
=> [1×(7-5√2)]/(7+5√2)(7-5√2)]
=> (7-5√2)/[(7+5√2)(7-5√2)]
=> (7-5√2)/[7²-(5√2)²]
Since , (a+b)(a-b) = a²-b²
Where , a = 7 and b = 5√2
=> (7-5√2)/(49-50)
=> (7-5√2)/(-1)
=> -7+5√2
=> 5√2-7
3).
Given that (x-2)³
This is in the form of (a-b)³
Where, a = x and b = 2
We know that
(a-b)³ = a³-3a²b+3ab²-b³
=> (x-2)³ = x³-3(x²)(2)+3(x)(2)²-2³
=> (x-2)³ = x³-6x²+12x-8
The coefficient of x² is -6