Akar akar persamaan px^2 - 3px + 5p -15 = 0 adalah A dan B. Jika A pangkat 3 + B pangkat 3 = 117 , .... Question from @ayusetyowatii

October 2018 2 344 Report

Akar akar persamaan px^2 - 3px + 5p -15 = 0 adalah A dan B.
Jika A pangkat 3 + B pangkat 3 = 117 , maka nilai p kuadrat + 1 ?

izharulhaq78 $\displaystyle (a+b)^3=a^3+3a^2b+3ab^2+b^3\\\left(a+b\right)^3=a^3+b^3+3ab(a+b)\\\left(\frac{-b}{a}\right)^3=117+3\left(\frac{c}{a}\right)\left(\frac{-b}{a}\right)\\\left(\frac{-(-3p)}{p}\right)^3=117+3\left(\frac{5p-15}{p}\right)\left(\frac{-(-3p)}{p}\right)\\(3)^3=117+3\left(\frac{5p-15}{p}\right)(3)\\27=117+9\left(\frac{5p-15}{p}\right)\\27-117=9\left(\frac{5p-15}{p}\right)\\-90=9\left(\frac{5p-15}{p}\right)\\-10p=5p-15\\-10p-5p=-15\\-15p=-15\\p=1\\\\p^2+1=1^2+1\\p^2+1=1+1\\\boxed{\boxed{p^2+1=2}}$

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Abdulhady $px^2-3px+(5p-15)=0\\\textup{Memiliki akar-akar a dan b}\\a^3+b^3=117\\p^2+1=....?\\\\a+b=- \frac{b}{a} \\a+b=3\\\\a.b= \frac{c}{a} \\a.b= \frac{5p-15}{p} \\\\(a+b)^3=a^3+b^3+3ab(a+b)\\(a+b)^3=a^3+b^3+3ab(3)\\27=117+9(\frac{5p-15}{p})\\-90=9(\frac{5p-15}{p})\\(\frac{5p-15}{p})=-10\\5p-15=-10p\\15p=15\\p=1\\\\p^2+1=1^2+1=2\\\\\boxed{\boxed{p^2+1=2}}$

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4 gram natrium hidroksida dilarutkan dengan air sampai massanya 100 gr ( diketahui mr NaOH = 40, air = 18, massa jenis air = 1 ) hitunglah a. Perseribu b. Normal

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