The value of the given expression [tex]x^7 + 64x^2 + 22[/tex] is 150.
What is an algebraic expression?
An algebraic expression is the combination of variables, coefficients, and constants.
Depending on the power/degree of the variable in the expression, the expressions are categorized into many types. Such as monomial, binomial, trinomial and polynomial.
Calculation:
It is given that,
[tex]x^3+4x=8[/tex]
Squaring on both sides:
[tex](x^3+4x)^2=8^2[/tex]
⇒ (x³)² + 2(x³)(4x) + (4x)² = 64
⇒ x⁶ + 8x⁴ + 16x² = 64
Multiplying by 'x' on both sides:
⇒ x(x⁶ + 8x⁴ + 16x²) = 64x
⇒ x⁷ + 8x⁵ + 16x³ = 64x
Adding 16x³ on both sides:
⇒ x⁷ + 8x⁵ + 16x³ + 16x³ = 64x + 16x³
⇒ x⁷ + 8x⁵ + 32x³= 64x + 16x³
On simplifying,
⇒ x⁷ + 8x² ( x³ + 4x)= 16(4x + x³)
On substituting x³ + 4x = 8;
⇒ x⁷ + 8x² (8)= 16(8)
⇒ x⁷ + 64x²= 128
Adding 22 on both sides:
⇒ x⁷ + 64x² + 22 = 128 + 22
⇒ x⁷ + 64x² + 22 = 150
Therefore, the value of the expression x⁷ + 64x² + 22 is 150.
Learn more about expressions here:
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