Jika x^1/2 + x^-1/2 = 2 maka x^3/2 + x^-3/2 = ?​

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Jika x^1/2 + x^-1/2 = 2 maka x^3/2 + x^-3/2 = ?​

EKponen

Penjelasan dengan langkah-langkah:

Jika x^1/2 + x^-1/2 = 2 maka x^3/2 + x^-3/2 = ?​

misalkan

sf x^{frac{1}{2}} =a dan x^{-frac{1}{2}} = b

sf a.b = x^{frac{1}{2}} . x^{-frac{1}{2}} = 1

a + b = 2

nilai dari
sf x^{frac{3}{2}} + x^{-frac{3}{2}} =a^3 + b^3

a³ + b³ =  (a + b){a² – ab + b²}
a³ + b³ =  (a + b){a²+ b²-  ab}
a³ + b³ =  (a + b) {(a+ b)² – 3ab}
a³ + b³ =  (2){ (2)² – 3(1)}
a³ + b³ =  (2){4-3}
a³ + b³ =  (2){1}
a³ + b³ =  2

sf x^{frac{3}{2}} + x^{-frac{3}{2}} =2

x^3/2 + x^-3/2 = a³ + b³

a³ + b³ = (a + b){a² – ab + b²}

a³ + b³ = (a + b) {(a+ b)² – 3ab}

a³ + b³ = (2)((2)² – 3(1)

a³ + b³ = 2

x^3/2 + x^-3/2 = 2