Question

(15+x)^2.(6+x)^2=136

Answer 1

(15+x)².(6+x)²=136

<=> [(15+x)(6+x)]²=6²

<=> (15+x)(6+x)=6

<=> 90+15x+6x+x²-6=0

<=> x²+21x+90=0

<=> (x+6)(x+15)=0

<=> x=\(\left[{}\begin{matrix}-6\\-15\end{matrix}\right.\)

Answer 2

(15 + x)² . (6 + x)² = 136

<=> (225 + 30x + x²)(36 + 12x + x²) = 136

<=> 8100 + 2700x + 225x² + 1080 + 360x² + 30x³ + 36x² + 12x³ + x⁴ = 136

<=> x⁴ + 30x³ + 12x³ + 225x² + 360x² + 36x² + 2700x + 8100 + 1080 = 136

<=> x⁴ + 42x³ + 621x² + 2700x + 9044 = 0

Do mik chưa hc PT bậc 4 nên mik ko giải tiếp đc, bn dùng máy tính giải tiếp nha.

Answer 3

(15+x)².(6+x)²=136

<=> [(15+x)(6+x)]²=(2\(\sqrt{34}\))²

<=> (15+x)(6+x)=2\(\sqrt{34}\)

<=> 90+15x+6x+x²- \(2\sqrt{34}\)=0

<=> x²+21x+90- \(2\sqrt{34}\)=0

<=> (x+6)(x+15)=0

<=> \(x\approx\left[{}\begin{matrix}-4,850\\-16,1490\end{matrix}\right.\)