Find the values of the following expressions- i-16x2-24x-9-when-x-7-4- ii-64x2-81y2-144xy-when-x-11-and-y-4-3- iii-81x2-16y2-72xy-when-x-2-3-and-y-3-4

(i) 16x^2+24x+9 =(4x)^2+2× 4x× 3+(3)^2 =(4x+3)^2 { a^2+2ab+b^2=(a+b)^2 } =(4×7/4+3 )^2=(7+3)^2 (∵ x=7/4 ) =(10)^2=100 (ii) 64x^2+81y^2+144xy =(8x) ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identities

Find the valu...

Question

Find the values of the following expressions:

$(i) 16 x^{2} + 24 x + 9, w h e n x = \frac{7}{4} (i i) 64 x^{2} + 81 y^{2} + 144 x y, w h e n x = 11 a n d y = \frac{4}{3} (i i i) 81 x^{2} + 16 y^{2} - 72 x y, w h e n x = \frac{2}{3} a n d y = \frac{3}{4}$

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Solution

$(i) 16 x^{2} + 24 x + 9 = (4 x)^{2} + 2 \times 4 x \times 3 + (3)^{2} = (4 x + 3)^{2} {a^{2} + 2 a b + b^{2} = (a + b)^{2}} = {(4 \times \frac{7}{4} + 3)}^{2} = (7 + 3)^{2} (∵ x = \frac{7}{4}) = (10)^{2} = 100 (i i) 64 x^{2} + 81 y^{2} + 144 x y = (8 x)^{2} + (9 y)^{2} + 2 \times 8 x \times 9 y = (8 x + 9 y)^{2} {∵ a^{2} + b^{2} + 2 a b = (a + b)^{2}} = {(8 \times 11 + 9 \times \frac{4}{3})}^{2} (∵ x = 11, y = \frac{4}{3}) = (88 + 12)^{2} = (100)^{2} = 10000 (i i i) 81 x^{2} + 16 y^{2} - 72 x y = (9 x)^{2} + (4 y)^{2} - 2 \times 9 x \times 4 y = (9 x - 4 y)^{2} {∵ a^{2} + b^{2} - 2 a b = (a - b)^{2}} = {(9 \times \frac{2}{3} - 4 \times \frac{3}{4})}^{2} {∵ x = \frac{2}{3}, y = \frac{3}{4}} = (6 - 3)^{2} = (3)^{2} = 9$

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Similar questions

Q. Find the values of the following expressions:
(i) 16x² + 24x + 9, when

x = \frac{7}{4}

(ii) 64x² + 81y² + 144xy, when x = 11 and

y = \frac{4}{3}

(iii) 81x² + 16y² − 72xy, when

x = \frac{2}{3}

and

y = \frac{3}{4}

Find the value of the expression

$(64 x^{2} + 81 y^{2} + 144 x y)$ when $x = 11$ and $y = \frac{4}{3}$

Q. Find the value of the expression (64x² + 81y² + 144xy), when x = 11 and

y = \frac{4}{3} .

Find $64 x^{2} + 81 y^{2} + \frac{144 x y}{48}$ when $x = 11$ and $y = \frac{4}{3}$

Q. Find the remainder when we divide

(9 x^{4} + 3 x^{3} y + 16 x^{2} y^{2} + 24 x y^{3} + 32 y^{4})

(3 x^{2} + 5 x y + 4 y^{2})

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Find the values of the following expressions: (i) 16x2+24x+9, when x=74(ii) 64x2+81y2+144xy, when x=11 and y=43(iii) 81x2+16y2−72xy, when x=23 and y=34

Find the values of the following expressions:

$(i) 16 x^{2} + 24 x + 9, w h e n x = \frac{7}{4} (i i) 64 x^{2} + 81 y^{2} + 144 x y, w h e n x = 11 a n d y = \frac{4}{3} (i i i) 81 x^{2} + 16 y^{2} - 72 x y, w h e n x = \frac{2}{3} a n d y = \frac{3}{4}$