kobel51 wrote:(sqr(2)+1)*(sqr(2)-1)*(sqr(3)+1)*(sqr(3)-1) =
A) 2
B) 3
C) 2*sqr(6)
D) 5
E) 6
I thought about estimating but seems like there should be a faster way
Always be on the lookout for the following quadratic identities:
(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
(a+b)(a-b) = a² - b².
The problem above is testing our ability to recognize the bottom identity, known as the DIFFERENCE OF TWO SQUARES:
(√2 + 1)(√2 - 1) *
(√3 + 1)(√3 - 1)
=
[ (√2)² - 1² ] *
[ (√3)² - 1² ]
=
(2-1)(3-1)
=
1*
2
= 2.
The correct answer is
A.
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