Question

what should be added to make each of the following a perfect square 1) 25 x square + 81...2) 81 x square minus 18 x 3) a to the power 4 + 1 by a to the power 4 ​

Answer 1

Answer:

1) +90x or -90x

2)+1

3)+2 or -2

Step-by-step explanation:

1)

25x^2+81

(5x)^2+(9)^2

we have a^2+b^2

we need 2ab to complete the square so

2×5x×9=90x

we will add 90x

to make (a+b)^2

(5x)^2+ (9)^2+90x= (5x+9)^2

similarly,

5x^2 (9)^2-90x=(5x-9)^2

2)

81x^2-18x

(9x)^2-2(9x)(1)

To make this a perfect square we need b

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

so b=1

we will add 1 to the given equation

(9x)^2-2(9x)(1)+(1)^2

=(9x-1)^2

3)

a^4 +(1÷a^4)

we will add 2 because 2AB =2×a^4×(1÷a^4)=2

a^4 +(1÷a÷4)+2

((a^2 +(1÷a^2))^2

a^4 + (1÷a^4) -2

((a^2)-(1÷a^2))^2

Answer 2

Step-by-step explanation:

hope it helps

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