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leonid [27]
3 years ago
15

Find x: (4x^2-25)^2-9(2x-5)^2=0

Mathematics
1 answer:
Feliz [49]3 years ago
6 0

Answer:

(4 {x}^{2}  - 25)^{2}  - 9(2x - 5)^{2}  = 0 \\  \\  {(4 {x}^{2}  - 25)} (4 {x}^{2} - 25)   - 9(2x - 5)(2x - 5) = 0 \\  \\( 16 {x}^{4}  - 200 {x}^{2}    + 625) - 9(4 {x}^{2}  - 20x + 25) = 0 \\  \\ (16 {x}^{4}  - 200 {x}^{2} + 625) + ( - 36 {x}^{2}  + 180x - 225) = 0 \\  \\ 16 {x}^{4}   - 236 {x}^{2}  + 180x + 400 = 0 \\  \\ 4(x + 1)(x + 4)(2x - 5)^{2}  = 0 \\  \\ x + 1 = 0 \\ x =  - 1 \\  \\ x + 4 = 0 \\ x =  - 4 \\  \\  {(2x - 5)}^{2}  = 0 \\ 2x - 5 = 0 \\ 2x = 5 \\ x =  \frac{5}{2}

I hope I helped you^_^

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