Question

Factorise using suitable identity 4x^2-36x+81

Answer 1

Answer:

$answer = \\ x = \frac{9}{2}$

Step-by-step explanation:

$4 {x}^{2} - 36x + 81 = 0 \\ 4 {x}^{2} - 18x - 18x + 81 = 0 \\ 2x(2x - 9) - 9(2x - 9) = 0 \\ (2x - 9)(2x - 9) =0 \\ (2x - 9 ) {}^{2} = 0 \\ 2x - 9 = 0 \\ x = \frac{9}{2}$

Answer 2

QUESTION:

Factorise using suitable identity 4x^2-36x+81

CONCEPT USED :

We can write as ;

$4 = {2}^{2}$

$81 = {9}^{2}$

now come to main question;

$4 {x}^{2} - 36x + 81$

$\red {(we \: can \: write \: this)}$

${(2x)}^{2} - 36x + {9}^{2}$

now middle term is written as;

$\orange {2 \times 2x \times 9}$

so we can use the identity here;

$\huge\blue {( {x - y})^{2}}$

the expansion of the identity is;

$\huge\pink {{x}^{2} - 2xy + {y}^{2}}$

so,

$( {2x - 9})^{2}$

$(2x - 9)(2x - 9) = 0$

hence,

$2x - 9 = 0 \\ 2x = 9 \\ x = \frac{9}{2}$

FINAL ANSWER:

$\huge\pink {x = \frac{2}{9}}$