Răspuns:
Explicație pas cu pas:
Formula : a² - b² = ( a - b ) ( a + b )
d) ( 2 x + √5)² - 45 = ( 2 x - 2√5 ) ( 2 x + 4√5)
→ notez cu a = 2 x + √5 si b = 45 = 3√5
= ( 2 x + √5 - 3√5 ) ( 2 x +√5 + 3√5) =
= ( 2 x - 2√5) ( 2 x + 4√5)
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e) 27 x² - ( 1 - √3 x)² = ( 4√3 x - 1 ) ( 2√3 x + 1 )
27 x² = a²; iar ( 1 - √3 x)² = b² ; aplic formula a² - b² si obtin:
= ( 3√3 x - 1 + √3 x ) ( 3√3 x + 1 - √3 x ) =
= ( 4√3 x - 1 ) ( 2√3 x + 1 )
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f) ( x + √2 y )²- 8 y² =( x - √2 y ) ( x + 3√2 y )
= ( x + √2 y - 2√2 y ) ( x + √2 y + 2√2 y) =
= ( x - √2 y ) ( x + 3√2 y )
