Question

y = (17 - x)(19 - x)(19 + x)(17 + x), when x is real, then the smallest possible value of 'y' is

I need explanation and step by step process

Answer 1

Answer:

x^4-650x^2+104329

Step-by-step explanation:

y=(17-x)(17+x)(19-x)(19+x)

(a-b)(a+b)=a^2-b^2

y=(17^2-x^2)(19^2-x^2)

=(289-x^2)(361-x^2)

=104329-289x^2-361x^2+x^4

= 104329-650x^2+x^4

x^4-650x^2+104329

Answer 2

Question

$\large{ \sf{y = (17 - x)(19 - x)(19 + x)(17 - x)}}$

Solution

Given Equation,

$\large{ \sf{y = (17 - x)(19 - x)(19 + x)(17 - x)}}$

Of the form,

a² - b² = (a + b)(a - b)

$\implies \: \sf{y = ( {17}^{2} - x {}^{2} )( {19}^{2} - {x}^{2} ) } \\ \\ \implies \: \sf{y = (289 - {x}^{2})(361 - {x}^{2} ) } \\ \\ \large{\implies \: \boxed{ \boxed{\sf{y = 104329 - 650 + {x}^{2} }}}}$

For smallest possible value of y,x should be equal to 0

$\longrightarrow \: \sf{y = 104329}$

Note

The negative integer,it would be converted into a positive numerical by the square function of x. Thus x = 0.