先閱讀下列第(1)題的解答過程:
(1)已知a,β是方程x
2+2x-7=0的兩個(gè)實(shí)數(shù)根,求a
2+3β
2+4β的值.
解法1:∵a,β是方程x
2+2x-7=0的兩個(gè)實(shí)數(shù)根,
∴a
2+2a-7=0,β
2+2β-7=0,且a+β=-2.
∴a
2=7-2a,β
2=7-2β.
∴a
2+3β
2+4β=7-2a+3(7-2β)+4β=28-2(a+β)=28-2×(-2)=32.
解法2:由求根公式得a=1+2
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,β=-1-2
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.
∴a
2+3β
2+4β=(-1+2
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)
2+3(-1-2
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)
2+4(-1-2
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)
=9-4
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+3(9+4
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)-4-8
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=32.
當(dāng)a=-1-2
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,β=-1+2
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時(shí),同理可得a
2+3β
2+4β=32.
解法3:由已知得a+β=-2,aβ=-7.
∴a
2+β
2=(a+β)
2-2aβ=18.
令a
2+3β
2+4β=A,β
2+3a
2+4a=B.
∴A+B=4(a
2+β
2)+4(a+β)=4×18+4×(-2)=64.①
A-B=2(β
2-a
2)+4(β-a)=2(β+a)(β-a)+4(β-a)=0.②
①+②,得2A=64,∴A=32.
請(qǐng)仿照上面的解法中的一種或自己另外尋注一種方法解答下面的問題:
(2)已知x
1,x
2是方程x
2-x-9=0的兩個(gè)實(shí)數(shù)根,求代數(shù)式x
13+7x
22+3x
2-66的值.