Toán Lớp 7: Cho a+b+c=0
a^2+b^2+c^2=1
Hỏi a^4+b^4+c^4= mấy
Nhanh
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Toán Lớp 7: Cho a+b+c=0
a^2+b^2+c^2=1
Hỏi a^4+b^4+c^4= mấy
Nhanh
Comments ( 2 )
Đáp án
Ta có:a+b+c=0=>(a+b+c)²=0
=>a²+b²+c²+2ab+2ac+2bc=0
=>1+2(ab+bc+ac)=0(vì a²+b²+c²=1)
=>ab+bc+cd=-1/2
=>(ab+bc+cd)²=1/4
=>a²b²+a²c²+b²c²+2a²bc +2ab²c+2abc²=1/4
=>a²b²+a²c²+b²c²+2abc(a+b+c)=1/4
=>a²b²
+a²c²+b²c²=1/4(vì a+b+c=0)*
Mặt khác a²+b²+c²=1(gt)
=>(a²+b²+c²)²=1
=>a⁴+b⁴+c⁴+2a²b²+2a²c²+2b²c²=1
=>a⁴+b⁴+c⁴+2(a²b²+a²c²+b²c²)=1
=>a⁴+b⁴+c⁴+2.1/4=1(theo *)
=>a⁴+b⁴+c⁴=1-1/2
=>a⁴+b⁴+c⁴=1/2