prep Math2 DS-90

[ggethan]

90. 8271-!-item-!-187;#058&006138
What is the value of a4 - b4 ?

(1) a2 - b2 = 16

(2) a + b = 8

答案(c)

為什麼不是(a)

這提到底問啥ㄚ 不懂

[vantreal]

a^4 - b^4
=(a^2+b^2)(a^2-b^2)
=(a^2+b^2)(a+b)(a-b)

(1) a^2 - b^2 = 16
we do not know the value of (a^2+b^2)
--> insufficient

(2) a + b = 8
we do not know the value of (a^2+b^2) and that of (a-b)
--> insufficient

(1)+(2)
a^2 - b^2 = 16
(a+b)(a-b) = 16
since a+b=8 (given), a-b=16/8=2
a+b=8,
a-b=2
then we can get a=5, b=3

since we now get both values of a and b,
(a^4 - b^4)=5^4-3^4=625-81=544 ---> sufficient

Ans: (C)

[ggethan]

原來是題目不清楚 我一直以為a4是4倍的a 原來是四次方

謝謝你啦 !!!!