Toán Lớp 7: a) x/3 = y/4 và xy = 192
b) x/5 = y/4 và x^2 – y^2 = 1
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Toán Lớp 7: a) x/3 = y/4 và xy = 192
b) x/5 = y/4 và x^2 – y^2 = 1
Comments ( 2 )
Đặt x/3=y/4=k
x/3=k=>x=3k
y/4=k=>y=4k
Lại có:
x.y=192
=>(3k).(4k)=192
=>(3.4).(k.k)=192
=>12.k^2=192
=>k^2=192:12
=>k^2=16
=>[(k^2=4^2),(k^2=(-4)^2):}
=>[(k=4),(k=-4):}
TH1:k=4
=>{(x=3k=3.4=12),(y=4k=4.4=16):}
TH2:k=-4
=>{(x=3k=3.(-4)=-12),(y=4k=4.(-4)=-16):}
Vậy (x;y)={(12;16);(-12;-16)}
b)
Đặt x/5=y/4=k
x/5=k=>x=5k
y/4=k=>y=4k
Lại có:
x^2-y^2=1
=>(5k)^2-(4k)^2=1
=>25k^2-16k^2=1
=>(25-16)k^2=1
=>9k^2=1
=>k^2=1/9
=>k=+-1/3
TH1:k=1/3
=>{(x=5k=5. 1/3=5/3),(y=4k=4 . 1/3=4/3):}
TH2:k=-1/3
=>{(x=5k=5.(-1)/3=-5/3),(y=4k = 4.(-1)/3=-4/3):}
Vậy (x;y)={(5/3;4/3);(-5/3;-4/3)}