Answered

Discover how IDNLearn.com can help you learn and grow with its extensive Q&A platform. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.

What is :

(49^x)(7^x^2)=2401^2

Sagot :

Lilithidn
[tex](49^x)(7 ^{x^2})=2401^2 \\ \\( (7^2)^x)(7 ^{x^2})= (7^4) ^2 \\ \\ 7 ^{2x}\cdot 7^{x^2}=7^{8} \\ \\ 7 ^{2x+x^2} =7^{8} \\ \\2x+x^2 =8[/tex]

 [tex]x^2-2x-8 = 0\\ \\ a=1, \ b=-2, \ c=-8 \\ \\\Delta =b^2-4ac = (-2)^2 -4\cdot1\cdot (-8) = 4 +32 =36 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{2-\sqrt{36}}{2 }=\frac{ 2-6}{2}=\frac{-4}{2}=-2 \\ \\x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{2+\sqrt{36}}{2 }=\frac{ 2+6}{2}=\frac{8}{2}= 4 \\ \\Answer: \ x=-2 \ \ or \ \ x=4[/tex]

Kate200468idn
[tex](49^x)(7^{x^2})=2401^2\\ \\7^{2x} \cdot7^{x^2}=(7^4)^2\\ \\7^{2x+x^2}=7^8\ \ \ \Leftrightarrow\ \ \ 2x+x^2=8\ \ \ \Leftrightarrow\ \ \ x^2+2x-8=0\\ \\x^2-2x+4x-8=0\ \ \ \Leftrightarrow\ \ \ x(x-2)+4(x-2)=0\\ \\(x-2)(x+4)=0\ \ \ \Leftrightarrow\ \ \ ( x-2=0\ \ \ \vee\ \ \ x+4=0)\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-4[/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.