giải pt x^2 -7x +30=6 căn (x+5)

 `x^2 - 7x + 30 = 6\sqrt[x+5] Với đk `: x ≥ -5`

` x^2 - 7x + 30 = 6\sqrt[x+5]`

`<=>  (x^2 - 7x + 30 )^2 = (6\sqrt[x+5])^2`

`<=> x^4 - 14x^3 + 109x^2 - 420x + 900 = 36x + 180`

`<=> x^4 - 14x^3 + 109x^2 - 456x + 720 = 0`

`<=> x^4 - 4x^3 - 10x^3 + 40x^2 + 69x^2 - 276x - 180x + 720 = 0`

`<=> x^3(x-4) - 10x^2(x - 4) + 69x(x - 4) - 180(x-4) = 0`

`<=> ( x^3 - 10x^2 + 69x - 180 )(x-4) = 0`

`<=> ( x^3 - 4x^2 - 6x^2 + 24x + 45x - 180)(x-4) = 0`

`<=> [x^2(x-4) - 6x(x-4) + 45(x-4) ](x-4) = 0`

`<=> (x-4)^2 ( x^2 - 6x + 45) = 0`

`<=> ( x-4)^2 = 0 (` Vì `x^2 - 6x + 45 = (x-3)^2 + 36 ≥ 36 )`

`<=> x = 4`