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# algebra

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Let a and b be the roots of the equation 2x^2+6x-14=0. What is the value of 3*a^5*b+a*b^5+2*a*b^5?

Jul 24, 2022

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What is the value of 3*a^5*b+a*b^5+2*a*b^5?

Hello Guest!

$$2x^2+6x-14=0\ |\ /2\\ x^2+3x-7=0\\ x=-1.5\pm \sqrt{2.25+7}\\ \{a,b\}=\{-4.541381,1.541381\}$$

$$3\cdot a^5\cdot b+a\cdot b^5+2\cdot a\cdot b^5\\ =3ab(a^4+b^4)\\ =3\cdot (-4.541381)\cdot 1.541381((-4.541381)^4+1.541381^4)\\ =-21(425.35531+5.64469)\\ =-21\cdot431\\ \color{blue}=-9051$$

!

Jul 24, 2022