Question

factorise using identify (5x-8)^2​

Answer 1

${\huge {\bold {\mathcal{\red {Answer:}}}}}$

$according \: to \: question \\ = > ({5x - 8})^{2} \\ identity \: used \\ (a + b)^{2} = {a}^{2} - 2 ab + {b}^{2}$

Now, we get

$( {5x - 8})^{2} = ({5x})^{2} - 2 \times 5x \times 8 + {8}^{2}$

$25 {x}^{2} - 80x + 64$

On solving this quaratic form

$25 {x}^{2} - 40x - 40x + 64$

on taking common

$5x(5x - 8 ) - 8(5x - 8)$

$(5x - 8)(5x - 8)$

so the value of

$x$

will be

$x = \frac{8}{5} \: \\ \: x = \frac{8}{5}$

Answer 2

Answer:

$\huge{\pink{\green{\sf{\therefore x=\frac{8}{5}}}}}$

Explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In this question information given about a quadratic.

▪We have to first factorise using identity and then find the value of x.

$\underline \bold{Given : }\\ \implies Factorise = ({5x - 8})^{2} \\ \\ \underline \bold{ To \: find : } \\ \implies Value \: of \: x = ?$

▪According to given question :

$\implies ( {5x - 8})^{2} = ({5x})^{2} + {8}^{2} - 2 \times 5x \times 8 \\ \underline \bold{by \: using \: identity : } \\ \implies ({a - b})^{2} = {a}^{2} + {b}^{2} - 2ab \\ \implies ({5x - 8})^{2} = 25 {x}^{2} + 64 - 80x \\ \underline \bold{for \: finding \: value \: of \: x : } \\ \implies 25 {x}^{2} - 80x + 64 = 0$

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$\underline \bold{By \: Quadratic \: Formula : } \\ \implies d = {b}^{2} - 4ac \\ \implies d = { ( - 80})^{2} - 4 \times 25 \times 64 \\ \implies d = 6400 - 6400 \\ \implies d = 0 \\ \\ \implies x = \frac{ - b + - \sqrt{d} }{2a} \\ \implies x = \frac{ - ( - 80) + - \sqrt{0} }{2 \times 25} \\ \implies x = \frac{80}{50} \\ \bold{\implies x = \frac{8}{5} }$

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