已知正实数xyzw满足2007^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求(根号2007x+2008y+2009z+2010w已知正实数xyzw满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求根号下(2007x+2008y+2009z+2010w )的值
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![已知正实数xyzw满足2007^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求(根号2007x+2008y+2009z+2010w已知正实数xyzw满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求根号下(2007x+2008y+2009z+2010w )的值](/uploads/image/z/1550236-4-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%AD%A3%E5%AE%9E%E6%95%B0xyzw%E6%BB%A1%E8%B6%B32007%5E2%3D2008y%5E2%3D2009z%5E2%3D2010w%5E2%2C%E4%B8%941%2Fx%2B1%2Fy%2B1%2Fz%2B1%2Fw%3D1%2C%E6%B1%82%28%E6%A0%B9%E5%8F%B72007x%2B2008y%2B2009z%2B2010w%E5%B7%B2%E7%9F%A5%E6%AD%A3%E5%AE%9E%E6%95%B0xyzw%E6%BB%A1%E8%B6%B32007x%5E2%3D2008y%5E2%3D2009z%5E2%3D2010w%5E2%2C%E4%B8%941%2Fx%2B1%2Fy%2B1%2Fz%2B1%2Fw%3D1%2C%E6%B1%82%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%882007x%2B2008y%2B2009z%2B2010w+%EF%BC%89%E7%9A%84%E5%80%BC)
已知正实数xyzw满足2007^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求(根号2007x+2008y+2009z+2010w已知正实数xyzw满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求根号下(2007x+2008y+2009z+2010w )的值
已知正实数xyzw满足2007^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求(根号2007x+2008y+2009z+2010w
已知正实数xyzw满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求根号下(2007x+2008y+2009z+2010w )的值
已知正实数xyzw满足2007^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求(根号2007x+2008y+2009z+2010w已知正实数xyzw满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x+1/y+1/z+1/w=1,求根号下(2007x+2008y+2009z+2010w )的值
设2007x²=2008y²=2009z²=2010z²=A ,
得到:2007x=A/x,2008y=A/y,2009z=A/z,2010w=A/w;
所以:2007x+2008y+2009z+2010w =A/x+A/y+A/z+A/w=A(1/x+1/y+1/z+1/w)=A.【2007x²】或【2008y²】或--------.
等于 √2007+√2008+√2009+√2010
令2007x^2=2008y^2=2009z^2=2010w^2=t^2
1/x=(√2007)/t
1/y=(√2008)/t
1/z=(√2009)/t
1/w=(√2010)/t
这4个式子相加 有 (√2007+√2008+√2009+√2010)/t=1
即 t=(√2007+...
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等于 √2007+√2008+√2009+√2010
令2007x^2=2008y^2=2009z^2=2010w^2=t^2
1/x=(√2007)/t
1/y=(√2008)/t
1/z=(√2009)/t
1/w=(√2010)/t
这4个式子相加 有 (√2007+√2008+√2009+√2010)/t=1
即 t=(√2007+√2008+√2009+√2010)
同时,有
2007x=t*√2007
2008y=t*√2008
2009z=t*√2009
2010w=t*√2010
这4个式子相加 有 2007x+2008y+2009z+2010w=t*(√2007+√2008+√2009+√2010)=t^2
所以 √(2007x+2008y+2009z+2010w)=√t^2=t=(√2007+√2008+√2009+√2010)
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提示2007x=(2007x^2)/x,其它类推
提出公因式得,2007x^2(1/x+1/y+1/z+1/w)