[tex]jika \: \alpha \: dan \: \beta \: \\ merupakan \: akar \: dari \: \: x²-5x-7=0. \: \\ tentukan \: nilai \: dari \frac{1 }{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} } [/tex]
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Jawaban:
39/49
Penjelasan dengan langkah-langkah:
terlampir
maaf jika salah
Materi : Bentuk dan Persamaan Kuadrat
x² - 5x - 7 = 0
__________/
x¹ + x² = -b/a = -(-5)/1 = 5
x¹ . x² = c/a = (-7)/1 = -7
___________________
1/(x¹)² + 1/(x²)²
= [ (x¹)² + (x²)² ]/( x¹ . x² )²
= [ ( x¹ + x² )² - 2( x¹ . x² ) ]/( x¹ . x² )²
= [ 5² - 2(-7) ]/(-7)²
= [ 25 + 14 ]/49
= 39/49
Semoga bisa membantu
[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]