1..the sum of a positive number and its square is 56.Find the number
2..the sum of the square of two consecutive positive odd number is 202.Find the two number,
我的英文好差。
吾識解題，^^
吾識兩條數學題，
2007-09-28 4:32 am
回答 (2)
2007-09-28 4:47 am
✔ 最佳答案
1.一个正数和它的平方數的总和是56.Find数字設它們的值x
x+x^2=56
x^2+x-56=0
(x+8)(x-7)=0
x= -8(rej.) OR x=7
x=7 因為要正數
2.二個連續正奇数的平方之和是202.找這二個数字
設其中一個奇数為x
則另一個奇数為x+2
x^2+(x+2)^2=202
2x^2+4x-198=0
(x+11)(x-9)=0
x= -11 (rej.) or x=9
x=9 (因為x為正數)
另一個是(9+2)
=11
2007-09-28 4:49 am
1) Let x be the no.
x + x^2 = 56
x = 7
2)Let x be the no.,x+2 be the other no.
x^2 + (x+2)^2 = 202
x^2 + (x^2 + 4x + 4) = 202
2x^2 + 4x + 4 = 202
2x^2 + 4x - 198 = 0
x^2 + 2x - 99 = 0
(x + 11)(x - 9) = 0
therefore,x = 9 or x = -11(rejected)
because x = 9 ,therefore,the two consecutive positive odd no. are 9 and (9+2)=11
x + x^2 = 56
x = 7
2)Let x be the no.,x+2 be the other no.
x^2 + (x+2)^2 = 202
x^2 + (x^2 + 4x + 4) = 202
2x^2 + 4x + 4 = 202
2x^2 + 4x - 198 = 0
x^2 + 2x - 99 = 0
(x + 11)(x - 9) = 0
therefore,x = 9 or x = -11(rejected)
because x = 9 ,therefore,the two consecutive positive odd no. are 9 and (9+2)=11
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