Maths guestions

1.If x^2 + x + 1 =5,則(2x+1)^2=
a.16
b.17
c.18
d.19
(2x+1)^2
=4x^2+4x+1
=4(x^2+x)+1
=4*4+1
=17
答案是b

2.If x+y=5 and xy=3, 則x^2+y^2=
a.17
b.18
c.19
d.20
x^2+y^2
=(x+y)^2-2xy
=25-6
=19
答案是c

3.化簡(49^x)(7^y)
a.49^xy
b.49^2x+y
c.7^2x-y
d.7^2x+y
(49^x)(7^y)
=(7^2)^x(7^y)
=7^(2x+y)
答案是d

4.在三角形ABC中,角B=2個角A-角C。求角A。
a.30
b.60
c.90
d.120
角B=2角A-角C
因角A+角B+角C=180
角A+2角A-角C+角C=180
3角A=180
角A=60
答案是b

5.若x^2-x=4,則(1-2x)^2=
a.16
b.17
c.18
d.19
(1-2x)^2
=1-4x+4x^2
=1+4(x^2-x)
=1+4*4
=17
答案是b

6.因式分解x^2-y^2-2y-1
a.(x-y+1)(x+y+1)
b.(x-y-1)(x+y-1)
c.(x+y-1)(x+y+1)
d.(x+y-1)(x-y-1)
x^2-y^2-2y-1
=x^2-(y+1)^2
=(x+y+1)(x-y-1)
無答案正確

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