Question

Вычислите наиболее рациональным способом



53^2 + 22^2 – 47^2 - 16^2 .

_______________

65^2 – 2 · 65 · 59 + 59^2



*это типо дробь

Answer 1

$\frac{53^{2}+22^{2}-47^{2}-16^{2}}{65^{2}-2*65*59+59^{2}} =\frac{(53^{2}-47^{2})+(22^{2}-16^{2})}{(65-59)^{2} }=\frac{(53-47)(53+47)+(22-16)(22+16)}{6^{2} }=\frac{6*100+6*38}{6^{2} }=\frac{6(100+38)}{6^{2} }=\frac{138}{6}=23$

Answer 2

53² + 22² – 47² - 16² / (65² – 2 • 65 • 59 + 59²)=

=(53²-47²)+(22²-16²) /(65-56)²=

=(53-47)(53+47)+(22-16)(22+16) / 9²=

=(6*100 +6*338 ) / 81=828/81=92/9=10  2/9