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Step-by-step explanation:
Given,
84 will be the product of her age before 2 years and after 3 years of her present age.
Let x be his present age,
Her age, two years ago will be (x-2)
Her age, three years hence will be (x+3)
According to the question,
{ c } { ( x - 2 ) \times ( x + 3 ) = 84 } \\\\ { ( x - 2 ) ( x + 3 ) = 84 } \\\\ { x ^ { 2 } + 3 x - 2 x - 6 = 84 } \\\\ { x ^ { 2 } + x - 6 = 84 }\ { x ^ { 2 } + x - 90 = 0 }
(x−2)×(x+3)=84
(x−2)(x+3)=84
x
2
+3x−2x−6=84
x
2
+x−6=84
x2+x−90=0
{ c } { x ^ { 2 } + 10 x - 9 x - 90 = 0 } { x ( x + 10 ) - 9 ( x + 10 ) = 0 } { ( x - 9 ) ( x + 10 ) = 0 } { x = 9 , x = - 10 }
x2 +10x−9x−90=0
x(x+10)−9(x+10)=0
(x−9)(x+10)=0
x=9,x=−10
Hence, we cannot represent age as a negative value. The value of x will be 9 only.
Answer:
1) since it is a rectangle
2y = x +4
x = 2y-4
4x - y = 2x +y +8
8y - 16 - y = 4y - 8 + y + 8
y = 4
x = 4 therefore it is a sq. since all side are equal
perimeter = 2(l+b) = 16
question 2) let the current age of ajay be x
x-2(x+3) = 84
x^2 +3x -2x -6 = 84
x^2 + x-90 =0
x^2 + 10x - 9x -90 = 0
x(x-10) - 9(x-10) =0
x=10 or 9