Question

(2x+5)(5x+2)=(3x+4)(5x+3)



PLEASE ANSWER FAST.
THANKS.​

Answer 1

★FIND:

${THE\: VALUE\:OF \:'X'.}$

★GIVEN,

➡️${(2x+5)(5x+2)=(3x+4)(5x+3)}$

★SOLUTION:

➡️${(2x+5)(5x+2)=(3x+4)(5x+3)}$

➡️${(10x^2++4x+25x+10=15x^2+9x+20x+12}$

➡️${10x^2+29x+10=15x^2+29x+12}$

➡️${15x^2-10x^2+29x-29x+12-10=0}$

➡️${5x^2+2=0}$.. EQ1

➡️${5x^2=-2}$

➡️${x^2=-2/5}$

➡️$x = + - \sqrt{ - 2 /5}$

➡️$x=+-\sqrt{2/5} i$ (since i=-1)

➡️$x=\sqrt{2/5}i$

Or

➡️$x=-\sqrt{2/5}i$

★VERIFICATION:

SUB, 'X' VALUE IN EQ1

(U CAN SUBSTITUTE IN GIVEN EQUATION ALSO BUT IT TAKE MORE STEPS)

➡️Sub,$x=+-\sqrt{2/5} i$ in EQ1

➡️${5x^2+2=0}$

➡️${5(\sqrt{2/5}i)^2+2}$

➡️${5(2/5)i^2+2}$

➡️${2i^2+2}$ (i^2=-1)

➡️${2(-1)+2}$

➡️${-2+2}$

➡️${0}$

Similarly sub, $x=-\sqrt{2/5}i$ in the EQ1, it will be equal to zero(0)

Answer 2

(2x+5) (5x+2) = (3x+4) (5x+3)

=> 10x²+4x + 25x+10 = 15x²+9x + 20x+12

=> 10x²-15x²+29x+10 = 29x+12

=> -5x²+29x-29x = 12-10

=> -5x² = 2

=> x² = 2/-5

=> x = √2/-5. ans.