Đáp án:
`a, x = (-53)/9`
`b, x=15`
Giải thích các bước giải:
`a,`
`3/(5×7) + 3/(7×9) + ... + 3/(x (x+2) ) = 24/35`
Điều kiện : `x \ne 0,x \ne -2`
`⇔ 3 × [1/(5×7) + 1/(7×9) + ... + 1/(x (x+2) )] = 24/35`
`⇔ 3 × 1/2 × [1/5 - 1/7 + 1/7 - 1/9 + ... + 1/x - 1/(x+2)]=24/35`
`⇔ 3/2 × [1/5 - 1/(x+2)]=24/35`
`⇔ 1/5 - 1/(x+2) = 24/35 ÷ 3/2`
`⇔ 1/5 - 1/(x+2)=16/35`
`⇔ 1/(x+2)=1/5 - 16/35`
`⇔1/(x+2)= (-9)/35`
`⇔ (x+2) × (-9) = 35`
`⇔ x+2=(-35)/9`
`⇔x=(-35)/9-2`
`⇔x=(-53)/9` (Thỏa mãn)
Vậy `x=(-53)/9`
`b,`
`1/10 + 1/40 + ... + 1/( (x+2) (x+5) )=3/20`
Điều kiện : `x \ne -2, x \ne -5`
`⇔ 1/(2×5) + 1/(5×8) + ... + 1/( (x+2) (x+5) ) = 3/20`
`⇔ 1/3× [1/2 - 1/5 + 1/5 - 1/8 + ... + 1/(x+2) - 1/(x+5) ]=3/20`
`⇔ 1/3 × [1/2 - 1/(x+5)]=3/20`
`⇔ 1/2 - 1/(x+5) = 3/20÷ 1/3`
`⇔ 1/2 - 1/(x+5)=9/20`
`⇔ 1/(x+5) =1/2 - 9/20`
`⇔ 1/(x+5)=1/20`
`⇔ x + 5 = 20`
`⇔x=20-5`
`⇔ x=15` (Thỏa mãn)
Vậy `x=15`