Question

1) Cho: 169(157-77x)² + 100(201-100x)² = 26(77x-157)(1000x-2010)

Tính giá trị của x

Answer 1

169.(157-77.x)^2 + 100.(201-100.x)^2 = 26.(77.x-157).(1000.x-2010) (1)
169.(157-77.x)^2 = (13 .(157-77.x)) ^2
100.(201-100.x)^2 = ( 2010- 1000x)^2
26.(77.x-157).(1000.x-2010) = 26.(157-77.x)( 2010- 1000x)
=> (1) <=> (13 .(157-77.x)) ^2 + ( 2010- 1000x)^2 - 26.(157-77.x)( 2010- 1000x) =0
<=> [ 13(157-77.x) - ( 2010- 1000x)]^2 =0 <=> 13(157-77.x) - ( 2010- 1000x) = 0

=> 2041-1001x-2010+1000x=0=>x=31