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If 3x-7y=10 and x y=-1, find the value ...

If `3x-7y=10 ` and `x y=-1,` find the value of `9x^2+49 y^2`

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To solve the problem, we need to find the value of \(9x^2 + 49y^2\) given the equations \(3x - 7y = 10\) and \(xy = -1\). ### Step-by-Step Solution: 1. **Start with the first equation:** \[ 3x - 7y = 10 \] ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If 9x^2+25 y^2=181\ \ a n d\ x y\ =\ -6, find the value of 3x+5y

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  2. If 2x+3y=8 and x y=2 , find the value of 4x^2+9y^2

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  3. If 3x-7y=10 and x y=-1, find the value of 9x^2+49 y^2

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  4. Simplify each of the products: (1/2a-3b)(1/2a+3b)(1/4a^2+9b^2)

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  5. Simplify each of the products: (m+n/7)^3 (m-n/7)

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  6. Simplify each of the products: (x/2-2/5)(2/5-x/2)-x^2+2x

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  7. Simplify each of the products: (x^2+x-2)(x^2-x+2)

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  8. Simplify each of the products: (x^3-3x^2-x)(x^2-3x+1)

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  9. Simplify each of the products: (2x^4-4x^2+1)(2x^4-4x^2-1)

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  10. Prove that a^2+b^2+c^2-a b-b c-c a is always non-negative for all valu...

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  11. Write the following in expanded form: (9x+2y+z)^2 (ii) (3x+2y-z)^2

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  12. Write the following in expanded form: (x-2y-3z)^2 (ii) (-x+2y+z)^2

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  13. Write the following in expanded form: (1/4a-1/2b+1)^2 (ii) (-2x+5y-...

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  14. Simplify: (a+b+c)^2+\ (a-b-c)^2

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  15. Simplify: (a+b+c)^2-(a-b-c)^2

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  16. If a^2+b^2+c^2=20 and a+b+c=0 , find a b+b c+c a

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  17. If a+b+c=9 and a b+b c+c a=40 , find a^2+b^2+c^2 Given:

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  18. If a^2+b^2+c^2=250 and a b+b c+c a=3 , find a+b+c ​

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  19. Write the following in the expanded form: (a+2b+c)^2 (ii) (2a-3b-c)...

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  20. Write the following in the expanded form: (-3x+y+z)^2 (ii) (m+2n-5p...

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