a,
`(2x+5)(2x-7)-(2x+3)^2=16`
`<=>4x^2-14x+10x-35-(4x^2+12x+9)-16=0`
`<=>4x^2-14x+10x-35-4x^2-12x-9-16=0`
`<=>-16x-60=0`
`<=>-16x=60`
`<=>x=-15/4`
Vậy `S={-15/4}`
b,
`(2x+3)^2-4(x-1)=49`
`<=>4x^2+12x+9-4x+4-49=0`
`<=>4x^2+8x-36=0`
`<=>4(x^2+2x-9)=0`
`<=>x^2+2x-9=0`
`<=>(x^2+2x+1)-10=0`
`<=>(x+1)^2-(\sqrt{10})^2=0`
`<=>(x+1+\sqrt10)(x+1-\sqrt10)=0`
`<=>` \(\left[ \begin{array}{l}x+1+\sqrt{10}=0\\x+1-\sqrt{10}=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=-1-\sqrt{10}\\x=-1+\sqrt{10}\end{array} \right.\)
Vậy `S={-1-\sqrt10 \ ; \ -1+\sqrt10}`
c,
`49x^2+14x+1=0`
`<=>(7x)^2+2.7x.1+1^2=0`
`<=>(7x+1)^2=0`
`<=>7x+1=0`
`<=>7x=-1`
`<=>x=-1/7`
Vậy `S={-1/7}`
d,
`16x^2-(4x-5)^2=15`
`<=>16x^2-(16x^2-40x+25)-15=0`
`<=>16x^2-16x^2+40x-25-15=0`
`<=>40x-40=0`
`<=>40x=40`
`<=>x=1`
Vậy `S={1}`
e,
`(8x^2+3)(8x^2-3)-(8x^2-1)^2=22`
`<=>(8x^2)^2-3^2-(64x^4-16x^2+1)-22=0`
`<=>64x^4-9-64x^4+16x^2-1-22=0`
`<=>16x^2-32=0`
`<=>16(x^2-2)=0`
`<=>x^2-2=0`
`<=>(x-\sqrt2)(x+\sqrt2)=0`
`<=>` \(\left[ \begin{array}{l}x-\sqrt{2}=0\\x+\sqrt{2}=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\sqrt{2}\\x=-\sqrt{2}\end{array} \right.\)
Vậy `S={\sqrt2;-\sqrt2}`
