Đáp án:
`5) x = 4`
`6) x ∈ {` `1/6` ; `17/6` `}`
Giải thích các bước giải:
`5)` $4^{x-2}$ `+` $4^{x+1}$ `= 1040`
`=>` $4^{x-3 + 1}$ `+` $4^{x- 3 + 4}$ `= 1040`
`=>` $4^{x-3}$ `. 4 +` $4^{x-3}$ . $4^{4}$ `= 1040`
`=>` $4^{x-3}$ `. ( 4 + 256 ) = 1040`
`=>` $4^{x-3}$ `= 1040 : 260`
`=>` $4^{x-3}$ `=` $4^{1}$
`=> x - 3 = 1`
`=> x = 4`
Vậy `x = 4`
`6)` `5/8` `- (` `3/4` `-` `1/2` `. x )² =` `13/72`
`=> (` `3/4` `-` `1/2` `. x )² =` `5/8` `-` `13/72`
`=> (` `3/4` `-` `1/2` `. x )² =` `45/72` `-` `13/72`
`=> (` `3/4` `-` `1/2` `. x )² =` `32/72`
`=> (` `3/4` `-` `1/2` `. x )² =` `4/9`
Trường hợp `1 :`
`(` `3/4` `-` `1/2` `. x )² = (` `2/3` `)²`
`=>` `3/4` `-` `1/2` `. x =` `2/3`
`=>` `1/2` `. x =` `3/4` `-` `2/3`
`=>` `1/2` `. x =` `9/12` `-` `8/12`
`=>` `1/2` `. x =` `1/12`
`=> x =` `1/12` `. 2`
`=> x =` `1/6`
Trường hợp `2 :`
`(` `3/4` - `1/2` `. x )² = ( -` `2/3` `)²`
`=>` `3/4` `-` `1/2` `. x = -` `2/3`
`=>` `1/2` `. x =` `3/4` `+` `2/3`
`=>` `1/2` `. x =` `9/12` `+` `8/12`
`=>` `1/2` `. x =` `17/12`
`=> x =` `17/12` `. 2`
`=> x =` `17/6`
Vậy `x ∈ {` `1/6` `;` `17/6` `}`
